AGEC FINAL P1, AGEC 3413 test 3 (chapter 6 done and half of 7), agec test 3 (just 10 for now)

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94) If there are 175 units demanded at destination 6, state the constraint for destination 6.

X46 + X56 = 175

A conditional constraint specifies the conditions under which variables are integers or real variables.

False

69) What is the optimal profit?

$1,240

67) What price for hit records will maximize the profit?

$44

117) How would the transshipment location constraints read if it was OK to store product there on a temporary basis?

AD + BD + CD - DF - DG - DH ≥ 0 AE + BE + CE - EF - EG - EH ≥ 0

69) Using all the nodes of interest for the entire menagerie, what is the maximal flow from Fruit to Hay? A) 16 B) 18 C) 20 D) 22

In a ________ integer model, the solution values of the decision variables are 0 or 1. A) total B) 0-1 C) mixed D) total, 0-1, and mixed

In a multiperiod scheduling problem, the production constraint usually takes the form of: A) beginning inventory + demand - production = ending inventory. B) beginning inventory - demand + production = ending inventory. C) beginning inventory - ending inventory + demand = production. D) beginning inventory + demand + production = ending inventory.

62) What is profit when the optimal values of potatoes and beets are produced? A) Z = 22 B) Z = 44 C) Z = 66 D) Z = 88

64) In the process of evaluating location alternatives, the transportation model method minimizes the: A) total demand. B) total supply. C) total shipping cost. D) number of destinations.

Balanced transportation problems have which of the following type of constraints? A) ≥ B) ≤ C) = D) <

T/F: In a mixed integer model, all decision variables have integer solution values.

Which of the following are assumptions or requirements of the transportation problem?

Goods are the same, regardless of source

A ________ integer model allows for the possibility that some decision variables are not integers.

Mixed

is a technique for selecting numbers randomly from a probability distribution.

Monte Carlo

Assuming that Si is a binary variable, the constraint for the first restriction is: S1 + S3 + S7 ≤1. S1 + S3 + S7 = 2. S1 + S3 + S7 ≥ 1. S1 + S3 + S7 ≤ 2.

S1 + S3 + S7 ≤ 2.

T/F: A feasible solution to an integer programming problem is ensured by rounding down non-integer solution values.

T/F: In a total integer model, all decision variables have integer solution values.

T/F: One type of constraint in an integer program is a multiple-choice constraint.

22) In solving the facility location problem, the objective is to locate a centralized facility that serves customers or other facilities such that the distance traveled between the facility and customers or other facilities is minimized.

TRUE

22) The source node is the input node in a maximal flow problem.

TRUE

6) For most real-world applications, an unbalanced transportation model is a more likely occurrence than a balanced transportation model.

TRUE

The three types of integer programming models are total, 0-1, and mixed. True or False

TRUE

74) Formulate the lawyer constraint for this scenario.

The lawyer constraint is as follows: 3X1 + 2X2 + 4X3 ≤ 5,000 where: X1 = 200 - 2.25p1 X2 = 300 - 3.00p2 X3 = 400 - 3.50p3

78) The model was entered into an Excel spreadsheet and the table below shows part of the sensitivity report. Calculate the expected per unit profit for the three services. (better chart in the document) Variable Cells Cell Name Final Value Reduced Gradient $C$3 P1_ 45.5694 0 $D$3 P2_ 51.5 0 $E$3 P3_ 58.8929 0

The model provides a solution that calls for only a sale price for P1 of $45.57 - coupled with its price of $2.25 means they make $43.32 per unit of X1. For item X2, the optimal price is $51.50, less the cost of $3, means Zevon makes $48.50 per unit. Finally, X3 will sell for $58.89, less the price of $3.50 means they realize a profit of $55.39 per unit.

Which of these constraints will ensure that a low capacity facility is not built in South America?

y12 + y22 = 0

methods assume that what has occurred in the past will continue to occur in the future.

Time series

In a ________ integer model, all decision variables have integer solution values. total 0-1 mixed all of the above

Total

93) If there are 300 units available at source 2, state the constraint for source node 2.

X24 + X25 = 300

118) Consider the network diagram given in Figure 3 with the indicated flow capacities along each branch. What is the input-output constraint associated with the fifth node of the network diagram for the 0-1 integer linear programming formulation of the maximal flow problem?

X25 + X35 + X65 - X56 - X57 = 0

32) Assume price and demand are related by the following function: v = 100 - 2.5p. If fixed cost = $5000 and variable cost = $10, then the expression for profit is ________.

Z = 125p - 2.5p2 - 6000

71) Determine the profit for the optimal production quantities of soap and shampoo.

Z = 18

85) Zoey's Catnip Toys faces the following relationship between price and demand: v = 2000 - 200p. The fixed cost is $500 and variable cost is $1. What price should Zoey charge to maximize profit?

$5.50

43) A branch where flow is permissible in either direction is a(n): A) directed branch. B) undirected branch . C) labeled branch. D) unlabeled branch.

Which of the following is not an integer linear programming problem? A) pure integer B) mixed integer C) 0-1 integer D) continuous

When the ________ command is used in an Excel spreadsheet, all the values in a column (or row) are multiplied by the values in another column (or row) and then summed.

SUMPRODUCT

T/F: In a 0-1 integer model, the solution values of the decision variables are 0 or 1.

T/F: The three types of integer programming models are total, 0-01, and mixed.

In adjusted exponential smoothing, the closer beta is to ________, the stronger a trend is reflected.

30) If a firm's profit is Z = 20p -2p2 + 40, then the optimal value of I yields a maximum profit of ________.

90 (p = 5)

61) The horse walks from the Grass to the Pond and the llamas walk from the Fruit to the Shade. How much longer does the horse walk if each takes the shortest possible route? A) 60' B) 50' C) 40' D) 35'

Which of the following will not decrease system utilization?

increase in arrival rate

A table of random numbers must be

efficiently generated.

Assume that we are using 0-1 integer programming model to solve a capital budgeting problem and xj = 1 if project j is selected and xj = 0, otherwise. The constraint (x1 + x2 + x3 + x4 = 2) means that ________ out of the ________ projects must be selected.

exactly 2, 4

22) In a(n) ________ problem, items are allocated from sources to destinations at a minimum cost.

transportation

In an unbalanced transportation model, supply does not equal demand, and supply constraints must have ≤ signs. True or False

FALSE

In a finite queue, the length of the queue is:

limited.

30) The goal of the ________ problem is to maximize the amount of flow of items from an origin to a destination.

maximal flow

31) A(n) ________ network model could be used to represent the capacity of a series of dams for flood control.

maximal flow

A limitation of simulation is that:

model building is costly and time-consuming

Simulation does not usually provide recommended decisions. Instead it provides:

operating characteristics

27) An example of a(n) ________ point is a distribution center or warehouse located between plants and stores.

transshipment

92) Consider the curve 10x2 + 4x - 7. What is the slope at x = 10?

204

T/F: The college dean is deciding among three equally qualified candidates for his associate dean position. If this situation can be modeled as an integer program, the decision variables would be cast as 0-1 integer variables.

T/F: The divisibility assumption is violated by integer programming.

Product mix problems cannot have greater-than-or-equal-to (≥) constraints. True or False

FALSE

The branch and bound solution method cannot be applied to 0-1 integer programming problems. True or False

FALSE

The branch and bound solution method cannot be applied to 0-1 integer programming problems.

False

The term big data refers to numbers of large magnitude, i.e., greater than or equal to one billion.

False

In a ________ integer model, all decision variables have integer solution values.

total

33) If price and demand are related by the function v = 15 + 15p and the fixed cost is $150 while the variable cost is $5, then the expression for profit is ________.

Z = 15 p2 - 60p - 225

The type of linear program that compares services to indicate which one is less productive or inefficient is called: A) product mix. B) data envelopment analysis. C) marketing. D) blending.

Which constraint best describes the situation with decision variables A and B? B - A = 0 B + A = 1 B - A ≤ 0 B + A ≤ 1

B - A = 0

48) David is qualified to teach Management Science, but has misplaced his slide rule and doesn't feel he can complete the necessary calculations if he is assigned to teach it next semester. Which of these constraints would ensure that he isn't the instructor? A) DI + DP + DQ + DC + DL ≥ 2 B) SM + GM + TM + DM ≤ 1 C) DM = 0 D) DI + DP + DQ + DC + DL + DM ≤ 3

60) Which of these routes for the horse is actually the shortest between the pair of nodes? A) Fruit - Hay = 160' B) Barn - Pond = 200' C) Grass - Pond = 190' D) Fruit - Shade = 165'

For a maximization integer linear programming problem, a feasible solution is ensured by rounding ________ non-integer solution values if all of the constraints are the less-than-or-equal-to type. A) up and down B) up C) down D) up or down

In a capital budgeting problem, if either project 1 or project 2 is selected, then project 5 cannot be selected. Which of the alternatives listed below correctly models this situation? A) x1 + x2 + x5 ≤ 1 B) x1 + x2 + x5 ≥ 1 C) x1 + x5 ≤ 1, x2 + x5 ≤ 1 D) x1 - x5 ≤ 1, x2 - x5 ≤ 1

46) Which constraint is appropriate for this scenario? A) DI + DP + DQ + DC + DL + DM = 2 B) SI + GI + TI + DI ≤ 6 C) SM + GM + TM + DM ≥ 1 D) SI + SP + SQ + SC + SL + SM ≤ 3

59) The constraint that represents the quantity demanded by Customer B is: A) 6X1B + 2X2B + 8X3B ≤ 350. B) 6X1B + 2X2B + 8X3B = 350. C) X1B + X2B + X3B ≤ 350. D) X1B + X2B + X3B = 350.

62) The horse decides that a small system of trails would be perfect for connecting his points of interest, the Grass, Barn, Hay and Pond along with the Oak. What is the minimal total path length for this construction project? A) 295' B) 290' C) 280' D) 270'

62) Which constraint represents the quantity shipped to retail outlet 6? A) X23 + X36 = 450 B) X23 + X36 + X26 = 450 C) X36 + X26 ≤ 450 D) X36 + X26 = 450 E) 3X36 + 5X26 = 450

64) Write the appropriate expression for the demand constraint. A) 2.5x1 = x2 B) x1 - 2.5x2 ≥ 0 C) x1 + 2.5x2 ≤ 0 D) x1 = 2.5x2

In a 0-1 integer programming model, if the constraint x1 - x2 = 0, it means when project 1 is selected, project 2 ________ be selected. A) can also B) can sometimes C) can never D) must also

The branch and bound method of solving linear integer programming problems is: A) an integer method. B) a relaxation method. C) a graphical solution. D) an enumeration method.

T/F: If we are solving a 0-1 integer programming problem, the constraint x1 ≤ x2 is a mutually exclusive constraint.

T/F: In a 0-1 integer programming problem involving a capital budgeting application (where xj = 1, if project j is selected, xj = 0, otherwise) the constraint x1 - x2 ≤ 0 implies that if project 2 is selected, project 1 cannot be selected.

T/F: In a mixed integer model, the solution values of the decision variables are 0 or 1.

T/F: The branch and bound solution method cannot be applied to 0-1 integer programming problems.

T/F: The management scientist's fiance informed him that if they were to be married, he would also have to welcome her mother into their home. The management scientist should model this decision as a contingency constraint.

15) The minimal spanning tree allows the visitation of each node without backtracking.

FALSE

indicates a forecast is biased high.

Large -

Sara's Sensible Critters makes two kinds of catnip toys: balls (x1) and mice (x2). The relationship between demand and price for balls and mice is: x1 = 1800 - 150p1 x2 = 1500 - 300p2 The cost for a catnip ball is $2 and for the mouse, $3. Sara has only 200 ounces of catnip on hand. A ball uses a tenth of an ounce and a toy mouse uses one-quarter of an ounce. 86) Write the formulation for this problem

Max Z = (p1 - 2)x1 + (p2 - 3)x2 s.t. 0.10x1 + 0.25x2 ≤ 200 Alternatively, Z = 2100p1 - 150p12 - 2400p2 - 300p22 - 8100

76) Formulate the objective function and constraints for this scenario.

Max Z = (p1 - 2.25)X1 + (p2 - 3)X2 + (p3 - 3.5)X3 subject to: 3X1 + 2X2 + 4X3 ≤ 5,000 7X1 + 5X2 + 6X3 ≤ 10,000 6X1 + 4X2 + 7X3 ≤ 15,000 where: X1 = 200 - 2.25p1 X2 = 300 - 3.00p2 X3 = 400 - 3.50p3 p1 = price of X1 p2 = price of X2 p3 = price of X3

________ variables are best suited to be the decision variables when dealing with yes-or-no decisions.

0-1

83) How many demand-side constraints are there? Write the demand-side constraints.

2 demand-side constraints x11 + x21 + x31 + x41 = 250 x12 + x22 + x32 + x42 = 250

The production manager for Beer etc. produces two kinds of beer: light (L) and dark (D). Two resources used to produce beer are malt and wheat. The manager can obtain at most 4800 oz of malt per week and at most 3200 oz of wheat per week, respectively. Each bottle of light beer requires 12 oz of malt and 4 oz of wheat, while a bottle of dark beer uses 8 oz of malt and 8 oz of wheat. Profits for light beer are $2 per bottle, and profits for dark beer are $1 per bottle. Which of the following is not a feasible solution?

300 L and 200 D

A rendering plant wishes to use the data (sales records from a few local businesses and the month of the year) to help determine their supply level for the coming months. The records shown in the table provide an excellent opportunity for you to assist them with their forecasting. What is the three-period weighted moving average for July using the weights 0.5 (most recent), 0.3, and 0.2?

45.6

29) If a firm's profit is Z = 100p -8p2 + 16, then the maximum profit occurs where p = ________.

6.25

Companies A, B, and C supply components to three plants (F, G, and H) via two crossdocking facilities (D and E). It costs $4 to ship from D regardless of final destination and $3 to ship to E regardless of supplier. Shipping to D from A, B, and C costs $3, $4, and $5, respectively, and shipping from E to F, G, and H costs $10, $9, and $8, respectively. Suppliers A, B, and C can provide 200, 300 and 500 units respectively and plants F, G, and H need 350, 450, and 200 units respectively. Crossdock facilities D and E can handle 600 and 700 units, respectively. Logistics Manager, Aretha Franklin, had previously used "Chain of Fools" as her supply chain consulting company, but now turns to you for some solid advice. 78) Which of these constraints allows for some inventory to be held at one of the crossdock facilities? A) AD + BD + CD - DF - DG - DH ≥ 0 B) AD + BD + CD - DF - DG - DH = 600 C) AD + BD + CD = DF - DG - DH = 600 D) AD + BD + CD + DF + DG + DH = 600

If a maximization linear programming problem consists of all less-than-or-equal-to constraints with all positive coefficients and the objective function consists of all positive objective function coefficients, then rounding down the linear programming optimal solution values of the decision variables will ________ result in a feasible solution to the integer linear programming problem. A) always B) sometimes C) optimally D) never

If we are solving a 0-1 integer programming problem, the constraint x1 + x2 = 1 is a ________ constraint. A) multiple-choice B) mutually exclusive C) conditional D) corequisite

In a ________ integer model, all decision variables have integer solution values. A) total B) 0-1 C) mixed D) total, 0-1, and mixed

Mondo's Runway Show Mondo Guerra is matching his models with his latest collection for Fashion Week. He has five models, ranging from 5'10" to 5'10.5" and size 0 to size 1. His five latest designs run the gamut from prêt-à-porter to an evening gown and he'd like to make sure each outfit looks as good as possible by having it worn on the runway by the right model. After an anxious month of sewing, he has each model try on each outfit and he assigns a fabulosity score to each combination as indicated in the table. (look at document for better chart) Gown Sport Couture Avant Garde Prêt-à-Porter Zoe 9 9 4 4 2 Yvette 3 8 3 8 9 Xena 4 7 3 7 8 Whisper 1 6 5 6 9 Vajay 4 9 9 6 7 38) What is an appropriate constraint for this scenario? A) ZG + ZS + ZC + ZA + ZP = 1 B) ZG + ZS + ZC + ZA + ZP ≤ 1 C) 9ZG + 9ZS + 4ZC + 4ZA + 2 ZP ≥ 1 D) 9ZG + 9ZS + 4ZC + 4ZA + 2 ZP = 1

Pro-Carpet company manufactures carpets in Northwest Indiana and delivers them to warehouses and retail outlets. The network diagram given in figure below shows the possible routes and distances from the carpet plant in Valparaiso to the various warehouses or retail outlets. V = Valparaiso, P = Portage, G = Gary, Ha = Hammond, Hi = Highland, M = Merillville, L = Lansing 52) What is the distance for the shortest route from the carpet plant in Valparaiso to retail outlet in Lansing, Illinois. State the total completion time in minutes. A) 36 B) 37 C) 39 D) 41

53) Determine the shortest route for a carpet delivery truck from the carpet plant in Valparaiso to retail outlet in Hammond. A) 26 B) 28 C) 30 D) 32

57) Which of the following are assumptions or requirements of the transportation problem? A) There must be multiple sources. B) Goods are the same, regardless of source. C) There must be multiple destinations. D) There must be multiple routes between each source and each destination.

77) Which of these assignments is optimal? A) Dean 1 addresses Curriculum B) Dean 2 tackles Development C) Dean 3 solves Assessment D) Deans 2 and 3 both work on the Budget

use management judgment, expertise, and opinion to make forecasts.

Qualitative methods

6) A profit function of Z = 3x2 - 12x + 5 reaches maximum profit at x = 2 units of output.

TRUE

Data envelopment analysis problems are usually maximization problems. True or False

TRUE

The college dean is deciding among three equally qualified (in their eyes, at least) candidates for his associate dean position. If this situation could be modeled as an integer program, the decision variables would be cast as 0-1 integer variables. True or False

TRUE

The divisibility assumption is violated by integer programming. True or False

TRUE

103) Mondo has never heard of linear programming and you don't have your laptop handy. Provide him with a "best case" total fabulosity number

The greatest possible value is 45, since there are 5 scores that will be chosen and the scores range from 1 to 9.

80) The model was entered into an Excel spreadsheet and the table below shows the answer report in its entirety. Show how the profit is calculated. (better chart in the document) Objective Cell (Max) Cell Name Original Value Final Value $F$4 Profit $5,638.13 $22,018.33 Objective Cell (Max) Cell Name Original Value Final Value Integer $C$3 P1_ $10.00 $45.57 Contin $D$3 P2_ $10.00 $51.50 Contin $E$3 P3_ $10.00 $58.89 Contin Constraints Cell Name Cell Value Formula Status Slack $F$8 Lawyers 1358.91 $F$8<=$I$8 Not Binding 3641.09 $F$9 Guns 2573.03 $F$9<=$I$9 Not Binding 7426.97 $F$10 Money 2523.94 $F$10<=$I$10 Not Binding 12476.06

The profit is a function of quantity sold and price, with the quantity sold a function of price. The X1 product has a demand of 200 - 2.25 × 45.57 = 97 The X2 product has a demand of 300 - 3 × 51.50 = 146 The X3 product has a demand of 400 - 3.5 × 58.89 = 194 The profit per X1 is $45.57 - 2.25 = $43.32 The profit per X2 is $51.50 - 3 = $48.50 The profit per X3 is $58.89 - 3.5 = $55.39 So 97 × $43.32 + 146 × $48.50 + 194 × 55.39 = $22,018.33

The Salt Creek Soap Company has determined the following nonlinear model to determine the optimal pounds of industrial soap (X1) and shampoo (X2) it should produce each day. Maximize Z = X12 + 2X22 - 8X1 - 12X2 + 34 Subject to: X1 + 2X2 = 4 lbs 70) Determine the quantity of soap and shampoo that should be produced to maximize profit.

X1 = 0, X2 = 2

The constraint for distribution center 1 is: X11 + X12 + X13 + X14 ≤ 500. X11 + X12 + X13 + X14 ≥ 500. X11 + X12 + X13 + X14D + 500y1 ≤ 0. X11 + X12 + X13 + X14 - 500y1 ≤ 0.

X11 + X12 + X13 + X14 - 500y1 ≤ 0.

97) What is the constraint for El Paso for the Mantastic problem?

X37 + X47 = 610

31) Assume price and demand are related by the following function: v = 200 - p. If fixed cost = $10,000 and variable cost = $8, then the expression for profit is ________.

Z = 208p - p2 - 11,600

84) Zoey's Catnip Toys faces the following relationship between price and demand: v = 2000 - 200p. The fixed cost is $500 and variable cost is $1. Write an expression for the total profit.

Z = 2200p - 200p2 - 2500

In a media selection problem, instead of having an objective of maximizing profit or minimizing cost, generally the objective is to maximize the ________.

audience exposure

A systematic approach to model formulation is to first:

define decision variables.

A technique that assumes certainty in its solution is referred to as:

deterministic.

37) The ________ the variability in an investment portfolio, the ________ the risk of the investment portfolio.

higher, higher OR lower, lower

If we are solving a 0-1 integer programming problem, the constraint x1 + x2 = 1 is a(n) ________ constraint.

multiple-choice

If we are solving a 0-1 integer programming problem, the constraint x1 + x2 ≤ 1 is a(n) ________ constraint.

mutually exclusive

20) Networks may be used to represent assignment problems.

true

Parameters are known, constant values that are usually coefficients of variables in equations

true

33) In most real-world cases, the supply capacity and demanded amounts result in a(n) ________ transportation model.

unbalanced

Which of these constraints would not be appropriate for this scenario? 2700x1 + 400x2 + 2500x3 + 1000x4 + 600x5 + 250x6 + 350x7 + 400x8 ≤ 3000 x3 + x4 = 1 1x1 + 2x2 + 1.5x3 + 3x4 + 0.5x5 + 1x6 + 0.25x7 + 0.5x8 ≤ 4 x1, x2, x3, x4, x5, x6 , x7, x8 ≥ 0 and integer

x1, x2, x3, x4, x5, x6 , x7, x8 ≥ 0 and integer

x11 + x12 ≤ 8000

107) Write the constraints for the 3 distribution centers.

x1A + x1B +x1c - 500y1 ≤ 0 x2A + x2B +x2c - 500y2 ≤ 0 x3A + x3B +x3c - 500y3 ≤ 0

66) What is the derivative of the profit function for the XYZ company? Simplify the terms as much as possible.

∂ Z/∂ p = -5p + 220

27) Assume a nonlinear programming problem with a single constraint has been solved. The value of the Lagrange multiplier is $0.75 and the value of the optimal profit (Z) is $25. If the right-hand side of the constraint is increased from 38 to 42, the new value of Z will be ________.

$28

A croissant shop produces two products: bear claws (B) and almond-filled croissants (C). Each bear claw requires 6 ounces of flour, 1 ounce of yeast, and 2 TS of almond paste. An almond-filled croissant requires 3 ounces of flour, 1 ounce of yeast, and 4 TS of almond paste. The company has 6600 ounces of flour, 1400 ounces of yeast, and 4800 TS of almond paste available for today's production run. Bear claw profits are 20 cents each, and almond-filled croissant profits are 30 cents each. What is the optimal daily profit?

$380

Cully Furniture buys two products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $500 and requires 100 cubic feet of storage space, and each medium shelf costs $300 and requires 90 cubic feet of storage space. The company has $75,000 to invest in shelves this week, and the warehouse has 18,000 cubic feet available for storage. Profit for each big shelf is $300 and for each medium shelf is $150. What is the maximum profit?

$45,000

28) If a nonlinear programming problem results in profit (Z) of $50, and the Lagrange multiplier for a constraint is -2, the new profit will be ________ if the right-hand side of the constraint is increased by 1 unit.

$48

116) What are the objective function terms that involve the demand locations?

$4DF + $4DG + $4DH + $10EF + $9EG + $8EH

$800

87) Consider the network diagram given in Figure 1. Assume that the amount on each branch is the distance in miles between the respective nodes. What is the shortest route from the source node (node 1) to nodes 5 and 6? Indicate the total distance for each route.

(node 1) - (node 2) - (node 3) - (node 5) : 13 miles (node 1) - (node 2) - (node 4) - (node 6): 13 miles

Figure 1. Delivery Routes 86) Consider the network diagram given in Figure 1. Assume that the amount on each branch is the distance in miles between the respective nodes. What is the shortest route from the source node (node 1) to nodes 2, 3, and 4? Indicate the total distance for each route.

(node 1) - (node 2): 6 miles (node 1) - (node 2) - (node 3): 8 miles (node 1) - (node 2) - (node 4): 11 miles

118) Sketch the network for this problem and label all nodes and arrows with the appropriate information.

(picture you need to look at in the document)

88) Write the assignment problem matrix below as a network flow problem. Assume that the numbers in each cell represent the travel distance required between nodes. The dash indicates that there is not a route between nodes. (BETTER CHART IN DOCUMENT) A B C 1 4 6 - 2 - 2 1 3 3 5 9

(picture you need to look at in the document)

Cars arrive at a single-bay car wash at an average of 6 per hour according to the Poisson distribution. The wash time is a constant 4 minutes. What is the average number of cars in line?

.133

The following data represents quarterly sales of lawnmowers. What is the seasonal index for the fourth quarter? (Round to the nearest hundredth.)

.25

A single-server waiting line system has an arrival pattern characterized by a Poisson distribution with 3 customers per hour. The average service time is 12 minutes. The service times are distributed according to the negative exponential distribution. The probability that the system is idle is:

.40.

Binary variables are:

0 or 1 only.

In a ________ integer model, the solution values of the decision variables are 0 or 1. total 0-1 mixed all of the above

0-1

_______ variables are best suited to be the decision variables when dealing with yes-or-no decisions.

0-1

In a ________ linear programming model, the solution values of the decision variables are zero or one.

0-1 integer

In a(n) ________ linear programming model, the solution values of the decision variables are zero or one.

0-1 integer

If the probability of an event is 0.36, what random number range specifies this properly?

0.30 - 0.40

120) If the origin node for this network is node number 1 and flow proceeds from node 1 to node 6, what is the shortest route through the network?

1 - 3 - 6 = 21

A graduate research assistant "moonlights" at the short order counter in the student union snack bar in the evenings. He is considering asking for help taking orders, but needs to convince the management that they should hire another student. Because he is taking a simulation class, he thinks it may be the perfect way to convince management to hire more help if he can show that customers have to wait a long time. When a customer arrives, he takes their order and their payment, prepares the food, gives it to the customer, and then takes the order from the next person in line. If someone arrives while he's cooking an order, they have to wait until he's completed the current order. He has simulated 5 orders. Average customer waiting time is:

1 minute

Companies A, B, and C supply components to three plants (F, G, and H) via two crossdocking facilities (D and E). It costs $4 to ship from D regardless of final destination and $3 to ship to E regardless of supplier. Shipping to D from A, B, and C costs $3, $4, and $5, respectively, and shipping from E to F, G, and H costs $10, $9, and $8, respectively. Suppliers A, B, and C can provide 200, 300 and 500 units respectively and plants F, G, and H need 350, 450, and 200 units respectively. Crossdock facilities D and E can handle 600 and 700 units, respectively. Logistics Manager, Aretha Franklin, had previously used "Chain of Fools" as her supply chain consulting company, but now turns to you for some solid advice. How many constraints are required to model this as a linear program?

Determine the maximal flow through the network in Figure 4. Assume that all branches are directed branches.

A horse and two llamas are discussing the key areas of their domain on a lazy summer afternoon. The llamas favor the pond and shade and like to browse the fruit trees and oaks on the property, making their way to the barn only when their owner favors them with some oats. The horse prefers to graze the grass and hay for food and drink from the pond but will race up to the barn when the owner is handing out oats up there. Between the three of them, they have stepped off the distances between many of these key points several times and believe that they have developed an accurate map, shown below. As incredible as it may seem, neither the horse nor the llamas have had any training in management science, which is where you come in. Llamas are pack animals and the owner occasionally has them tote supplies from the fruit trees down to the hay stand. What is the shortest route between the two?

155'

Administrators at a university will charge students $150 to attend a seminar. It costs $3000 to reserve a room, hire an instructor, and bring in the equipment. Assume it costs $25 per student for the administrators to provide the course materials. How many students would have to register for the seminar for the university to break even?

A horse and two llamas are discussing the key areas of their domain on a lazy summer afternoon. The llamas favor the pond and shade and like to browse the fruit trees and oaks on the property, making their way to the barn only when their owner favors them with some oats. The horse prefers to graze the grass and hay for food and drink from the pond but will race up to the barn when the owner is handing out oats up there. Between the three of them, they have stepped off the distances between many of these key points several times and believe that they have developed an accurate map, shown below. As incredible as it may seem, neither the horse nor the llamas have had any training in management science, which is where you come in. The horse decides that a small system of trails would be perfect for connecting his points of interest, the Grass, Barn, Hay and Pond along with the Oak. What is the minimal total path length for this construction project?

270'

A horse and two llamas are discussing the key areas of their domain on a lazy summer afternoon. The llamas favor the pond and shade and like to browse the fruit trees and oaks on the property, making their way to the barn only when their owner favors them with some oats. The horse prefers to graze the grass and hay for food and drink from the pond but will race up to the barn when the owner is handing out oats up there. Between the three of them, they have stepped off the distances between many of these key points several times and believe that they have developed an accurate map, shown below. As incredible as it may seem, neither the horse nor the llamas have had any training in management science, which is where you come in. The llamas decide that a small system of trails would be perfect for connecting their points of interest, the Fruit, Barn, Hay, Shade, Pond and the Oak. What is the minimal total path length for this construction project?

270'

Taco Loco is considering a new addition to their menu. They have test marketed a number of possibilities and narrowed them down to three new products, X, Y, and Z. Each of these products is made from a different combination of beef, beans, and cheese, and each product has a price point. Taco Loco feels they can sell an X for $17, a Y for $13, and a Z for $14. The company's management science consultant formulates the following linear programming model for company management. The sensitivity report from the computer model reads as follows: How many pounds of beans will Taco Loco have left over if they produce the optimal quantity of products X, Y, and Z?

28.73

The college director of global activities was hopeful that the print ads in the school newspaper and 30 second spots on the campus radio station would spur some interest in the array of study tour and study abroad options he had secured. The communications director for the college had other ideas; she favored a social media campaign consisting of tweets and facebook postings. "This is the most ridiculous thing I ever heard of," he whined to the dean. The communications director's market research revealed the following: The advertising budget is $3500, but there is no requirement that all the money be spent. The newspaper has only four issues before the end of the semester, but the radio is a 24/7 operation and has two dozen 30 second slots available. Facebook postings must be alternated with the rest of the mindless drivel posted on the college page; thus there is space for only three postings before the end of the semester. Twitter is complicated by the 140 character requirement. The communications director feels she needs five tweets to convey a single message about tours and semesters abroad, so for one message, the cost would be $25 for each of the five components of the single ad. Due to thumb fatigue, she feels that she has only 2800 characters left in her thumbs before the end of the semester. (A side note - During the intersession period, she plans to embark on a strict regimen of thumb yoga to prepare for the coming semester.) Which of these is an appropriate constraint for this scenario?

500N + 250R + 125T + 15F ≤ 3,500

Companies A, B, and C supply components to three plants (F, G, and H) via two crossdocking facilities (D and E). It costs $4 to ship from D regardless of final destination and $3 to ship to E regardless of supplier. Shipping to D from A, B, and C costs $3, $4, and $5, respectively, and shipping from E to F, G, and H costs $10, $9, and $8, respectively. Suppliers A, B, and C can provide 200, 300 and 500 units respectively and plants F, G, and H need 350, 450, and 200 units respectively. Crossdock facilities D and E can handle 600 and 700 units, respectively. Logistics Manager, Aretha Franklin, had previously used "Chain of Fools" as her supply chain consulting company, but now turns to you for some solid advice. Which of these is not an element of the objective function?

600D

75) Formulate the financial constraint for this scenario.

6X1 + 4X2 + 7X3 ≤ 15,000 where: X1 = 200 - 2.25p1 X2 = 300 - 3.00p2 X3 = 400 - 3.50p3 p1 = price of X1 p2 = price of X2 p3 = price of X3

Captain Stubing of The Pacific Princess seeks to maximize the return for their scheduled 14 day tour of Europe and has a number of options available to him. He can ply his guests with alcohol, upsell them on fancier restaurant fare or include more expensive excursion options. These alternatives are not without tradeoffs, since different guests prefer different options, depending largely on their age and wherewithal. Among the limitations Captain Stubing must consider is the number of excursions; they must offer at least five alternatives per day for each the ten days they will reach port. In addition, the restaurant choices must exceed 12 major styles of cuisine and the bar themes down in The Grotto should rotate every other day for the 14 days. It's possible to rotate them twice a day, but any more than that and poor Isaac spends more time tearing down and setting up than he does mixing libations. Ideally, there should be at least one different bar theme for every cuisine type. The total budget for excursions, restaurants and bar has been set by the parent company at $150,000. It costs $1,500 to stock supplies for a major cuisine category, it costs $5,000 to include each different excursion, and it costs $900 to set up with a different bar theme. Based on historical data, Captain Stubing believes that each new bar setup will generate $1,500 profit, each new cuisine type will bring in $5,000, and each excursion type will generate $17,000 for the ship. What is the appropriate constraint for the budget?

900 Bar + 1500 Food + 5,000 Excursion ≤ 150,000

39) What is an appropriate constraint for this scenario? A) ZG + YG + XG + WG + VG ≤ 1 B) ZG + YG + XG + WG + VG = 1 C) 9ZG + 3YG + 4XG + 1WG + 4VG ≥ 1 D) 9ZG + 3YG + 4XG + 1WG + 4VG = 1

42) Mondo ran the problem in Excel and has copied a portion of the sensitivity report below. (look at document for better chart) Cell Name Final Value Reduced Cost Objective Coefficient Allowable Increase AllowableDecrease $J$13 Zoe Gown 1 0 9 1E+30 3 $K$13 Zoe Sport 0 0 9 3 2 $L$13 Zoe Leisure 0 -2 4 2 1E+30 $M$13 Zoe Cocktail 0 -5 4 5 1E+30 $N$13 Zoe Pret a Porter 0 -8 2 8 1E+30 What is a reasonable conclusion that can be drawn from this section of the report? A) Zoe will contribute 9 points to the overall fabulosity score of the model. B) It doesn't matter whether Zoe wears the sport outfit or the gown. C) The sport outfit has a range of 5 in fabulosity. D) Wearing the cocktail dress would lower the overall fabulosity score by 5 points.

46) Classical optimization is the use of ________ to determine the optimal value of a variable. A) calculus B) linear programming C) nonlinear programming D) goal programming

47) The shipping company manager wants to determine the best routes for the trucks to take to reach their destinations. This problem can be solved using the: A) shortest route solution technique. B) minimal spanning tree solution method. C) maximal flow solution method. D) minimal flow solution method.

47) Which constraint ensures that Introduction to Operations is offered according to the scenario? A) SI + GI + TI + DI ≥ 6 B) SI + GI + TI + DI ≤ 6 C) SI + SP + SQ + SC + SL + SM ≤ 6 D) SI + SP + SQ + SC + SL + SM ≥ 6

50) The Lagrange multiplier is ________ to the dual variables in a linear programming problem. A) analogous B) contradictory C) inversely related D) opposite

58) Consider the following network, which shows the location of various facilities within a youth camp and the distances (in tens of yards) between each facility. There is a swampy area between facilities A and E. Walking trails will be constructed to connect all the facilities. In order to preserve the natural beauty of the camp (and to minimize the construction time and cost), the directors want to determine which paths should be constructed. What is the minimum number of paths (in tens of yards) that must be built to connect each facility? A) 54 B) 56 C) 60 D) 65

61) Schrute Farms has determined the following nonlinear model to determine the optimal pounds of potatoes (X1) and beets (X2) it should produce each day. Maximize Z = + 2 - 8X1 + 12X2 + 34 Subject To: X1 + 2X2 = 4 tons What quantities of potatoes and beets maximize profit? A) X1 = 0, X2 = 2 B) X1 = 1, X2 = 2 C) X1 = 2, X2 = 2 D) X1 = 2, X2 = 1

70) The constraint for Knoxville is: A) X14 + X24 + X34 - X43 - X45 - X46 - X47 = 0. B) X13 + X23 - X35 - X36 - X37 ≥ 0. C) X14 + X24 + X34 - X45 - X46 - X47 = 0. D) X14 + X24 + X34 + X43 + X45 + X46 + X47 ≥ 0.

72) The first step of the maximal flow solution method is to: A) arbitrarily select any path in the network from origin to destination. B) select the node with the shortest direct route from the origin. C) add the maximal flow along the path to the flow in the opposite direction at each node. D) select any starting node.

81) Which of these is the shortest route through the network? A) 1-3-6 B) 1-2-5-6 C) 1-4-5-6 D) 1-2-4-5-6

Binary variables are: A) 0 or 1 only. B) any integer value. C) any continuous value. D) any negative integer value.

Let: rj = regular production quantity for period j, oj = overtime production quantity in period j, ij = inventory quantity in period j, and dj = demand quantity in period j. Correct formulation of the demand constraint for a multiperiod scheduling problem is: A) rj + oj + i2 - i1 ≥ dj. B) rj + oj + i1 - i2 ≥ dj. C) rj + oj + i1 - i2 ≤ dj. D) rj - oj - i1 + i2 ≥ dj.

Companies A, B, and C supply components to three plants (F, G, and H) via two crossdocking facilities (D and E). It costs $4 to ship from D regardless of final destination and $3 to ship to E regardless of supplier. Shipping to D from A, B, and C costs $3, $4, and $5, respectively, and shipping from E to F, G, and H costs $10, $9, and $8, respectively. Suppliers A, B, and C can provide 200, 300 and 500 units respectively and plants F, G, and H need 350, 450, and 200 units respectively. Crossdock facilities D and E can handle 600 and 700 units, respectively. Logistics Manager, Aretha Franklin, had previously used "Chain of Fools" as her supply chain consulting company, but now turns to you for some solid advice. 114) Write every constraint that involves Company A.

A's supply constraint is AD + AE = 200 D's balance constraint is AD + BD + CD - DF - DG - DH = 0 E's balance constraint is AE + BE + CE - EF - EG - EH = 0

Companies A, B, and C supply components to three plants (F, G, and H) via two crossdocking facilities (D and E). It costs $4 to ship from D regardless of final destination and $3 to ship to E regardless of supplier. Shipping to D from A, B, and C costs $3, $4, and $5, respectively, and shipping from E to F, G, and H costs $10, $9, and $8, respectively. Suppliers A, B, and C can provide 200, 300 and 500 units respectively and plants F, G, and H need 350, 450, and 200 units respectively. Crossdock facilities D and E can handle 600 and 700 units, respectively. Logistics Manager, Aretha Franklin, had previously used "Chain of Fools" as her supply chain consulting company, but now turns to you for some solid advice. Which of these constraints allows for some inventory to be held at one of the crossdock facilities?

AD + BD + CD - DF - DG - DH ≥ 0

49) Copied below is a portion of the answer report that shows the constraints related to the faculty assignment. Which of these statements is best according to the answer report? (look at document for better chart) Cell Name Cell Value Formula Status Slack $S$15 Saba_assigned 3 $S$15<=$Q$15 Binding 0 $S$15 Saba_assigned 3 $S$15>=$T$15 Not Binding 1 $S$16 Geoff_assigned 3 $S$16<=$Q$16 Binding 0 $S$16 Geoff_assigned 3 $S$16>=$T$16 Not Binding 1 $S$17 Tim_assigned 2 $S$17<=$Q$17 Not Binding 1 $S$17 Tim_assigned 2 $S$17>=$T$17 Binding 0 $S$18 David_assigned 3 $S$18<=$Q$18 Binding 0 A) Geoff is assigned to teach Introduction to Operations. B) Tim is assigned to teach two courses. C) David is assigned to teach Management Science. D) Saba is assigned to teach two courses.

51) In a transportation problem, items are allocated from sources to destinations: A) at a maximum cost. B) at a minimum cost. C) at a minimum profit. D) at a minimum revenue.

52) It was a bumper crop for hominy this year, and The Hominy Man hoped to set a price for a case that maximized profit. The annual fixed cost for the hominy harvesting and other equipment is $10,000 and the variable cost per case is $0.50. The price is related to demand according to the following equation: v = 800 - 16p. What is the optimal price of a case of hominy that will maximize the profit? A) $16.16 B) $25.25 C) $37.37 D) $44.44

55) Which of these is the lawyer constraint for this scenario? A) 7X1 + 5X2 + 6X3 ≤ 10,000 B) 3X1 + 2X2 + 4X3 ≤ 5,000 C) 6X1 + 4X2 + 7X3 ≤ 15,000 D) X1 = 200 - 2.25p1

56) The assignment problem constraint x41 + x42 + x43 + x44 ≤ 3 means: A) agent 3 can be assigned to 4 tasks. B) agent 4 can be assigned to 3 tasks. C) a mixture of agents 1, 2, 3 and 4 will be assigned to tasks 1, 2 or 3. D) There is no feasible solution.

59) The model is entered in Excel and the sensitivity report reveals that all of the constraints' Lagrange multipliers are zero. The impact for Zevon is: A) The profit for this scenario cannot be maximized. B) Not all of the lawyers they have available will be used. C) The demand for service X1 exceeds Zevon's ability to supply it. D) The profit generated by service X1 is not a function of demand for X1.

63) In an assignment problem all supply and demand values equal are: A) 0. B) 1. C) 2. D) greater than 1.

63) The llamas decide that a small system of trails would be perfect for connecting their points of interest, the Fruit, Barn, Hay, Shade, Pond and the Oak. What is the minimal total path length for this construction project? A) 275' B) 270' C) 265' D) 260'

65) The assignment problem constraint x31 + x32 + x33 + x34 ≤ 2 means: A) agent 3 can be assigned to 2 tasks. B) agent 3 can be assigned to no more than 2 tasks. C) a mixture of agents 1, 2, 3 and 4 will be assigned to tasks. D) agents 1, 2, 3, and 4 can be assigned up to 2 tasks.

66) In an assignment problem: A) one agent can do parts of several tasks. B) one task can be done by only one agent. C) each agent is assigned to its own best task. D) several agents can do parts of one task.

73) The shortest route problem requires: A) each destination to be visited only once. B) finding the quickest route from the source to each node. C) that there be a branch from each destination to every other destination. D) that there be no two-way branches between nodes.

73) Which of these changes in the original formulation of the Mantastic problem will result in no transfer of product from Philadelphia to Knoxville? A) increasing the cost to ship product from Philadelphia to Knoxville to $14 per unit. B) lowering the cost to ship product from Philadelphia to New Orleans to $12 per unit. C) increasing the cost to ship product from Philadelphia to Knoxville to $16 per unit. D) lowering the cost to ship product from Philadelphia to either New Orleans or Memphis to $12 per unit.

79) Which of these is not an element of the objective function? A) 4DF B) 600D C) 9EG D) 3CE

80) What is the shortest route through the network in Figure 4. A) 16 B) 18 C) 20 D) 22

82) This network has been targeted for the innovative new "Elimination of Redundancy Elimination" program that offers a compromise between two competing factions. The plan is to remove paths one at a time until all of the nodes are interconnected without any loops in the network while minimizing the sum of all of the path lengths. Which of these paths is part of the new network? A) 3-6 B) 1-3 C) 1-2 D) 2-5

Comedy Pasture A horse and two llamas are discussing the key areas of their domain on a lazy summer afternoon. The llamas favor the pond and shade and like to browse the fruit trees and oaks on the property, making their way to the barn only when their owner favors them with some oats. The horse prefers to graze the grass and hay for food and drink from the pond but will race up to the barn when the owner is handing out oats up there. Between the three of them, they have stepped off the distances between many of these key points several times and believe that they have developed an accurate map, shown below. As incredible as it may seem, neither the horse nor the llamas have had any training in management science, which is where you come in. 59) Llamas are pack animals and the owner occasionally has them tote supplies from the fruit trees down to the hay stand. What is the shortest route between the two? A) 150' B) 155' C) 160' D) 165'

If we are solving a 0-1 integer programming problem, the constraint x1 + x2 ≤ 1 is a ________ constraint. A) multiple-choice B) mutually exclusive C) conditional D) corequisite

In a 0-1 integer programming model, if the constraint x1 - x2 ≤ 0, it means when project 2 is selected, project 1 ________ be selected. A) must always B) can sometimes C) can never D) is already

In formulating a mixed integer programming problem, the constraint x1 + x2 ≤ 500y1 where y1 is a 0-1 variable and x1 and x2 are continuous variables, then x1 + x2 = 500 if y1 is: A) 0. B) 1. C) 0 or 1. D) none of the above

Mantastic Devices designs and manufactures high-end support garments for men. The facilities in Manhattan and Atlanta serve as design and component manufacturing facilities. Components are then shipped to warehouses in Philadelphia or Knoxville, where they are held until final assembly is completed at either Memphis, New Orleans, or El Paso. Manufacturing capacity in Manhattan and Atlanta is 900 units. Demand at Memphis, New Orleans, and El Paso is 450, 500, and 610, respectively. The network representing the shipping routes is shown below. (picture you need to look at in the document) The costs for shipping between each facility is shown below. A blank cell indicates that shipping between two facilities is not permitted. (BETTER CHART IN DOCUMENT) Philadelphia Knoxville Memphis New Orleans El Paso Manhattan $4 $25 Atlanta $22 $3 Philadelphia $3 $20 $30 $40 Knoxville $3 $6 $15 $20 68) The transshipment locations are: A) Manhattan and Atlanta. B) Philadelphia and Knoxville. C) Manhattan, Atlanta, Philadelphia and Knoxville. D) Memphis, New Orleans, and El Paso.

Semester Prep The department chair reviewed last year's schedule, the degree requirements for the ever popular Operations and Supply Chain major, and the emails that had drifted into her mailbox over the last week. Naturally, every professor in the department had his own pet course and wanted to maintain control of it while avoiding 8 a.m. classes at all costs. In an effort to placate the senior faculty members of the department, the chair sent an email asking them to supply the prep time for each of the classes they were qualified to teach, promising to assign them the least taxing schedule possible. Each of her department members had to teach at least two courses, but no more than three. The elective courses, Project Management, Quality Management, Control and Planning, Logistics, and Management Science each had to be offered once and the department needed to offer at least six sections of the Introduction to Operations class. The prep times each professor estimated for each course appear in the table below. (look at document for better chart) Intro to Ops Project Mgt Quality Mgt Control Logistics Mgt Science Saba 3 10 12 16 12 7 Geoff 4 19 2 10 8 18 Tim 5 11 4 14 14 3 David 4 11 4 15 17 15 45) What is an appropriate objective function for this scenario? A) Max Z = 3SI + 10SP + 12SQ + 16SC + 12SL + 7SM + 4GI + 19GP + 2GQ + 10GC + 8GL + 18GM + 5TI + 11TP + 4TQ + 14TC + 14TL + 3TM + 4DI + 11DP + 4DQ + 15DC + 17DL + 15DM B) Min Z = 3SI + 10SP + 12SQ + 16SC + 12SL + 7SM + 4GI + 19GP + 2GQ + 10GC + 8GL + 18GM + 5TI + 11TP + 4TQ + 14TC + 14TL + 3TM + 4DI + 11DP + 4DQ + 15DC + 17DL + 15DM C) Min Z = SI + SP + SQ + SC + SL + SM + GI + GP + GQ + GC + GL + GM + TI + TP + TQ + TC + TL + TM + DI + DP + DQ + DC + DL + DM D) Max Z = SI + SP + SQ + SC + SL + SM + GI + GP + GQ + GC + GL + GM + TI + TP + TQ + TC + TL + TM + DI + DP + DQ + DC + DL + DM

B = 150, M = 0

________ types of linear programming problems often result in fractional relations between variables which must be eliminated.

Blending

40) Which term does not belong in an objective function for this scenario? A) 9WP B) 4XG C) 6XC D) 9ZG

45) If we wanted to represent an office layout as a network flow problem, which of the following would be represented as a branch? A) offices B) waiting areas C) heating and ventilation systems D) computer rooms

50) Copied below is a portion of the answer report that shows the status of the variable cells related to the faculty assignment. Which of these statements is consistent with the answer report? (look at document for better chart) Cell Name Original Value Final Value Integer $J$15 Saba Intro 1 2 Contin $K$15 Saba Project Mgt 1 0 Contin $L$15 Saba Quality Control 1 0 Contin $M$15 Saba Planning/Control 1 0 Contin $N$15 Saba Logistics 1 0 Contin $O$15 Saba Mgt Science 1 1 Contin $J$16 Geoff Intro 1 0 Contin A) Geoff is assigned to teach Introduction to Operations. B) Tim is assigned to teach two courses. C) David is assigned to teach Introduction to Operations D) Saba is assigned to teach two courses.

51) The Lagrange multiplier is: A) the shadow price for the constraint coefficients. B) valid over a range of changes in the RHS. C) the rate of change in the objective value as the RHS of the constraint increases. D) the minimum threshold for decision variables to enter the solution.

54) The problem that deals with the distribution of goods from several sources to several destinations is the: A) network problem. B) assignment problem. C) transportation problem. D) transshipment problem.

56) The local Internet provider wants to develop a network that will connect its server at its satellite center in Valparaiso with the main city computer centers in Northwest Indiana to improve the Internet service and to minimize the amount of cable used to connect network nodes. If we represent this problem with a network: A) the cities are branches and cables are nodes. B) the cables are the branches and the cities are the nodes. C) the length of cables in miles are the branches, and the cities are the nodes. D) the cities are the branches and the length of cables in miles are the nodes.

56) Which of these is the money constraint for this scenario? A) 7X1 + 5X2 + 6X3 ≤ 10,000 B) 3X1 + 2X2 + 4X3 ≤ 5,000 C) 6X1 + 4X2 + 7X3 ≤ 15,000 D) X1 = 200 - 2.25p1

57) Consider the network diagram given in Figure 2. Assume that the numbers on the branches indicate the length of cable (in miles) six nodes on a telecommunication network. What is the minimum number of miles of cable to be used to connect all six nodes? Figure 2 A) 16 miles B) 17 miles C) 18 miles D) 19 miles

60) The analytics gurus at Zevon realize that they had misformulated their demand curves. They now believe that demand for X1 is given by 1000 - 2.25p1, demand for X2 is given by 2000 - 3p2, and demand for X3 is given by 3000 - 3.5p3. This model is entered in Excel and the sensitivity report contains the following: (better chart in the document) Constraints Cell Name Final Value Lagrange Multiplier $F$8 Lawyers 5000.00 101.052 $F$9 Guns 9275.74 0 $F$10 Money 9213.49 0 What is the best conclusion from the list below? A) The profit for this scenario cannot be maximized. B) Not all of the lawyers they have available will be used. C) If Zevon can retain the services of another lawyer for less than $101, they should do so. D) Lawyer jokes aside, Zevon cannot benefit from hiring additional lawyers at any cost.

64) The llamas and horse spend most of their day wandering back and forth among their favorite spots in the yard, and have worn paths that are two feet wide among them. Amazingly, these paths correspond to a minimal spanning tree network! The property owner is fearful that the bare dirt paths will wash out during heavy rains, so he initiates a soil conservation project to lay sod over all of the bare dirt paths. How many square feet of sod must he purchase? A) 1080 B) 540 C) 680 D) 820

67) The difference between the assignment and the transportation problem is that: A) total supply must equal total demand in the assignment problem. B) the number of origins must equal the number of destinations in the transportation problem. C) each supply and demand value is 1 in the assignment problem. D) both A and B

68) Using the nodes of interest for the horse, Grass, Barn, Oak, Hay and Pond, what is the maximal flow from the Grass to Hay? A) 11 B) 12 C) 13 D) 14

75) Which of the following constraints represents the assignment for assistant dean 2? A) X2A + X2B + X2C + X2D ≤ 1 B) X2A + X2B + X2C + X2D = 0 C) X2A + X2B + X2C + X2D = 1 D) X2A + X2B + X2C + X2D ≥ 0

76) Consider the network diagram given in Figure 3 with the indicated flow capacities along each branch. Determine the maximal flow on the following path: node 1 to node 4 to node 6 to node 8 to node 9. A) 2 B) 3 C) 4 D) 5

An interim dean needs help from three assistant deans after the dean and associate dean were transferred back to full-time faculty. The estimated time for each assistant dean to do each task is given in the matrix below. (BETTER CHART IN DOCUMENT) Assessment Budget Curriculum Development Assistant 1 44 54 42 45 Assistant 2 48 50 64 47 Assistant 3 46 56 64 72 74) How many tasks will be assigned to the assistant deans? A) 1 task B) 2 tasks C) 3 tasks D) 4 tasks

Assume that x2, x7 and x8 are the dollars invested in three different common stocks from New York Stock Exchange. In order to diversify the investments, the investing company requires that no more than 60% of the dollars invested can be in "stock 2." The constraint for this requirement can be written as: A) x2 ≥ .60. B) x2 ≥ .60 (x2 + x7 + x8). C) .4x2 - .6x7 - .6x8 ≤ 0. D) .4x2 - .6x7 - .6x8 ≥ 0.

Comedy Pasture II A horse and two llamas are discussing the key areas of their domain on a lazy summer afternoon. The llamas favor the pond and shade and like to browse the fruit trees and oaks on the property, making their way to the barn only when their owner favors them with some oats. The horse prefers to graze the grass and hay for food and drink from the pond but will race up to the barn when the owner is handing out oats up there. Between the three of them, they have stepped off the distances between many of these key points several times and believe that they have developed an accurate map, shown below. This map shows the number of loads that can be hauled between all connected points on the property. As incredible as it may seem, neither the horse nor the llamas have had any training in management science, which is where you come in. 65) Using the nodes of interest for the llamas, Fruit, Barn, Oak, Shade, Hay and Pond, what is the maximal flow from the Barn to the Pond? A) 17 B) 18 C) 20 D) 23

Consider the following network representation of shipment routes between plants, a distribution center, and retail outlets. The numbers next to the arcs represent shipping costs. For example, the cost of shipping from plant 1 to distribution center 3 is equal to $2. (picture you need to look at in the document) Assume that Plant 1 can supply 400 units and Plant 2, 500 units. Demand at the retail outlets are: Outlet 4, 300 units; Outlet 5, 250 units; Outlet 6, 450 units. 61) Which constraint represents transshipment through the distribution center? A) 2X13 + 3X23 = 900 B) 2X13 + 3X23 + 5X34 + 4X35 + 3X36 = 0 C) X13 + X23 - X34 - X35 - X36 = 0 D) X13 + X23 - X34 - X35 - X36 ≥ 0

In a ________ integer model, some solution values for decision variables are integers and others can be non-integer. A) total B) 0-1 C) mixed D) total, 0-1, and mixed

In a portfolio problem, X1, X2, and X3 represent the number of shares purchased of stocks 1, 2, and 3, which have selling prices of $15, $47.25, and $110, respectively. The investor has up to $50,000 to invest. The stockbroker suggests limiting the investments so that no more than $10,000 is invested in stock 2 or the total number of shares of stocks 2 and 3 does not exceed 350, whichever is more restrictive. How would this be formulated as a linear programming constraint? A) X2 ≤ 10000, X2 + X3 ≤ 350 B) 10,000 X2 ≤ 350X2 + 350X3 C) 47.25X2 ≤ 10,000, X2 + X3 ≤ 350 D) 47.25X2 ≤ 10,000, 47.25 X2 + 110X3 ≤ 350

Let xij = gallons of component i used in gasoline j. Assume that we have two components and two types of gasoline. There are 8000 gallons of component 1 available, and the demand gasoline types 1 and 2 are 11,000 and 14,000 gallons, respectively. Write the supply constraint for component 1. A) x21 + x22 ≤ 8000 B) x12 + x22 ≥ 8000 C) x11 + x12 ≤ 8000 D) x21 + x22 ≥ 8000

Max Z = 13x1 + 8x2 Subject to: 15x1 + 12x2 ≤ 144 7x1 + 9x2 ≤ 64 x1, x2 ≥ 0 and integer What is the optimal solution? A) x1 = 5, x2 = 6, Z = 113 B) x1 = 7, x2 = 7, Z = 147 C) x1 = 9, x2 = 0, Z = 117 D) x1 = 0, x2 = 15, Z = 120

Captain Stubing should exhaust his Budget.

is the percentage of the variation in the dependent variable that results from the independent variable.

Coefficient of determination

(FIGURE) 119) Using the network shown and the conventional method discussed in your textbook, what are the first two nodes in the network and why? Now avoid convention and pick the first two nodes that must be part of the correct solution. Why is this the case?

Convention dictates that a solution begins with node 1 and proceeds to the nearest node, which is node 3 at a distance of 11. Tossing convention out, one should pick the two closest nodes, which in this network are nodes 4 and 5, separated by only 6 units.

35) ________, a measure of correlation between returns on investment i and returns on investment j is used to reflect risk.

Covariance

41) What is the best overall fabulosity score that Mondo can hope for? A) 9 B) 25 C) 36 D) 45

54) The minimal spanning tree problem determines the: A) minimum amount that should be transported along any one path. B) maximum amount that can be transported along any one path. C) shortest distance between a source node and a destination node. D) minimum total branch lengths connecting all nodes in the network.

55) In the linear programming formulation of a transportation network: A) there is one variable for each arc. B) there is one constraint for each node. C) the sum of variables corresponding to arcs out of a source node is constrained by the supply at that node. D) All of these statements are correct for the linear programming formulation.

57) The model is entered in Excel and executes to reveal that p1 equals $45.57. Which of these conclusions is correct? A) The per unit profit for X1 is $45.57. B) The contribution to net profit from service X1 is $4,441.59. C) There is excess demand for service X1. D) The demand for X1 is 97.

60) In a transshipment problem, items may be transported: A) from destination to destination. B) from one transshipment point to another. C) directly from sources to destinations. D) all of the above

67) Using the nodes of interest for the horse, Grass, Barn, Oak, Hay and Pond, what is the maximal flow from the Grass to Pond? A) 11 B) 12 C) 13 D) 14

71) The objective function is: A) MAX 4X13 + 25X14 + 22X23 + 3X24 - 3X34 - 3X43 - 20X35 - 30X36 - 40X37 - 6X45 - 15X46 - 20X47. B) MIN 4X13 + 25X14 + 22X23 + 3X24 - 3X34 - 3X43 - 20X35 - 30X36 - 40X37 - 6X45 - 15X46 - 20X47. C) MAX 4X13 + 25X14 + 22X23 + 3X24 + 3X34 + 3X43 + 20X35 + 30X36 + 40X37 + 6X45 + 15X46 + 20X47. D) MIN 4X13 + 25X14 + 22X23 + 3X24 + 3X34 + 3X43 + 20X35 + 30X36 + 40X37 + 6X45 + 15X46 + 20X47.

74) The maximal flow algorithm: A) does not require flow on every branch for the final solution. B) may end with capacity remaining at the source. C) may end with capacity at those nodes leading immediately to the destination. D) all of the above

76) Which of the following constraints represents the assignment for the curriculum task? A) X1C + X2C + X3C ≥ 1 B) X1C + X2C + X3C = 0 C) X1C + X2C + X3C = 1 D) X1C + X2C + X3C ≤ 1

79) Determine the minimum distance required to connect all nodes in Figure 4. A) 22 B) 24 C) 26 D) 30

80) How many decision variables are in this problem? A) 8 B) 9 C) 10 D) 12

84) If the two shortest paths in this network are increased by 100%, and the two longest paths in this network are reduced by 50%, what is the shortest route through this network? A) 10.5 B) 17.5 C) 19.5 D) 21

Compared to blending and product mix problems, transportation problems are unique because: A) they maximize profit. B) the constraints are all equality constraints with no "≤" or "≥" constraints. C) they contain fewer variables. D) the solution values are always integers

Figure 2 50) Consider the network diagram given in Figure 2. Assume that the amount on each branch is the distance in miles between the respective nodes. What is the distance for the shortest route from the source node (node 1) to node 4? A) 8 B) 9 C) 10 D) 11

If a maximization linear programming problem consists of all less-than-or-equal-to constraints with all positive coefficients and the objective function consists of all positive objective function coefficients, then rounding down the linear programming optimal solution values of the decision variables will ________ result in a(n) ________ solution to the integer linear programming problem. A) always, optimal B) always, non-optimal C) never, non-optimal D) sometimes, optimal

If we are solving a 0-1 integer programming problem, the constraint x1 = x2 is a ________ constraint. A) multiple-choice B) mutually exclusive C) conditional D) corequisite

Quickbrush Paint Company is developing a linear program to determine the optimal quantities of ingredient A and ingredient B to blend together to make oil-base and water-base paint. The oil-base paint contains 90 percent A and 10 percent B, whereas the water-base paint contains 30 percent A and 70 percent B. Quickbrush currently has 10,000 gallons of ingredient A and 5,000 gallons of ingredient B in inventory and cannot obtain more at this time. Assuming that x represents the number of gallons of oil-base paint, and y represents the gallons of water-base paint, which constraint correctly represents the constraint on ingredient A? A) .9A + .1B ≤ 10,000 B) .9x + .1y ≤ 10,000 C) .3x + .7y ≤ 10,000 D) .9x + .3y ≤ 10,000

he department chair reviewed last year's schedule, the degree requirements for the ever popular Operations and Supply Chain major, and the emails that had drifted into her mailbox over the last week. Naturally, every professor in the department had his own pet course and wanted to maintain control of it while avoiding 8 a.m. classes at all costs. In an effort to placate the senior faculty members of the department, the chair sent an email asking them to supply the prep time for each of the classes they were qualified to teach, promising to assign them the least taxing schedule possible. Each of her department members had to teach at least two courses, but no more than three. The elective courses, Project Management, Quality Management, Control and Planning, Logistics, and Management Science each had to be offered once and the department needed to offer at least six sections of the Introduction to Operations class. The prep times each professor estimated for each course appear in the table below. David is qualified to teach Management Science, but has misplaced his slide rule and doesn't feel he can complete the necessary calculations if he is assigned to teach it next semester. Which of these constraints would ensure that he isn't the instructor?

DM = 0

The department chair reviewed last year's schedule, the degree requirements for the ever popular Operations and Supply Chain major, and the emails that had drifted into her mailbox over the last week. Naturally, every professor in the department had his own pet course and wanted to maintain control of it while avoiding 8 a.m. classes at all costs. In an effort to placate the senior faculty members of the department, the chair sent an email asking them to supply the prep time for each of the classes they were qualified to teach, promising to assign them the least taxing schedule possible. Each of her department members had to teach at least two courses, but no more than three. The elective courses, Project Management, Quality Management, Control and Planning, Logistics, and Management Science each had to be offered once and the department needed to offer at least six sections of the Introduction to Operations class. The prep times each professor estimated for each course appear in the table below. Copied below is a portion of the answer report that shows the status of the variable cells related to the faculty assignment. Which of these statements is consistent with the answer report?

David is assigned to teach Introduction to Operations

102) The llamas are interested in developing a series of llama-only paths among their points of interest. As they have a limited budget, they'd prefer to develop those paths using a minimum quantity of materials and labor. Formulate an objective function for this scenario using a linear programming model.

Decision variables are represented by an alphabetic ordering of the two node, e.g., the Barn-Fruit path is decision variable BF. Min Z = 20BF + 80BO + 110BS + 95FO + 300FP + 60HO + 60HP + 50HS + 90OP + 70OS

T/F: If we are solving a 0-1 integer programming problem, the constraint x1 = x2 is a conditional constraint.

T/F: In the classic game showPassword, the suave, silver-haired host informed the contestants, "you can choose to pass or to play." This expression suggests a mixed integer model is most appropriate.

T/F: Rounding non-integer solution values up to the nearest integer value will result in an infeasible solution to an integer linear programming problem.

100) A clean-up crew is stationed at facility F and wants to take the shortest route to each site. They usually clean up facilities B and A on the same day and therefore want the shortest route from F to each facility. Recommend a route for the crew to leave from F, clean up each facility A and B, and then return to facility F. (Assume all paths are accessible.)

F-E-G-B-D-A-C-F for a total of 80. (This is a small version of the traveling salesmen problem. Doing the minimal spanning tree prior to this problem may be helpful.). The clean-up crew may want to add additional facilities on the days they clean up A and B if they have time.

1) Nonlinear programming has the same format as linear programming, however either the objective function or the constraints (but not both) are nonlinear functions.

FALSE

10) In an unbalanced transportation problem, if demand exceeds supply, the optimal solution will be infeasible.

FALSE

10) The first derivative of a cost function equals zero at the point V = 100. This is definitely the worst output volume for the producer to choose.

FALSE

11) Decision variables cannot be multiplied by each other in the objective function of a nonlinear program.

FALSE

11) The first step of the minimal spanning tree solution to compute the distance of any path through the network.

FALSE

13) An optimal solution to a nonlinear programming problem will always occur at the boundary of the feasible solution space formed by the constraint.

FALSE

13) In a minimal spanning tree, the source and destination nodes must be connected along a single path.

FALSE

14) The choice of the initial node in the minimal spanning tree technique must be the first node.

FALSE

16) Both linear and nonlinear programming models have the general form of an objective function subject to more than 1 constraint.

FALSE

16) The shortest route network problem could help identify the best plan for running cables for televisions throughout a building.

FALSE

18) If a nonlinear program has been correctly formulated, procedures guarantee a solution.

FALSE

18) Regardless of the number of nodes in a network, the minimal spanning tree cannot contain the two nodes with the greatest distance between them.

FALSE

2) In a transportation problem, items are allocated from sources to destinations at a maximum value.

FALSE

20) Constraints for nonlinear programs are usually nonlinear.

FALSE

20) The shortest route problem requires that there be a branch from each destination to every other destination.

FALSE

21) In a transshipment model, the supply at each source and demand at each destination are limited to one unit.

FALSE

21) The maximal flow algorithm may end with capacity remaining at the source.

FALSE

5) Flows in a network can only be in one direction.

FALSE

5) In an unbalanced transportation model, all constraints are equalities.

FALSE

5) The slope of a curve at its highest point equals 1.

FALSE

7) In order to model a "prohibited route" in a transportation or transshipment problem, the route should be omitted from the linear program.

FALSE

8) A firm has a cost function of 3x2 - 25x + 374. Without having two examples of their output volume and total cost, we cannot determine their fixed cost.

FALSE

8) A prohibited route in a transportation model should be assigned a value of zero.

FALSE

8) The shipping company manager wants to determine the best routes for the trucks to take to reach their destinations. This problem can be solved using the minimal spanning tree.

FALSE

9) Maximum profit is achieved everywhere the first derivative of the profit function equals zero.

FALSE

A conservative approach to a balanced transportation model would be to make all constraints less-than-or-equal-to constraints. True or False

FALSE

A linear programming model of a media selection problem is used to determine the relative value of each advertising media. True or False

FALSE

Double-subscripted variables are required when there are two decision variables. True or False

FALSE

Fractional relationships among variables are considered standard form in a blending problem. True or False

FALSE

In Excel, a binary constraint in cell A1 is created using the =BIN($A$1) formula. True or False

FALSE

In a 0-1 integer programming problem involving a capital budgeting application (where xj = 1, if project j is selected, xj = 0, otherwise) the constraint x1 - x2 ≤ 0 implies that if project 2 is selected, project 1 cannot be selected. True or False

FALSE

In the classic game show Password, the suave, silver-haired host informed the contestants, "you can choose to pass or to play." This expression suggests a mixed integer model is most appropriate. True or False

FALSE

The constraint x + y = z is written in standard form. True or False

FALSE

The management scientist's fiancé informed him that if they were to be married, he would also have to welcome her mother into their home. The management scientist should model this decision as a contingency constraint. True or False

FALSE

Transportation problems can have solution values that are non-integer and must be rounded. True or False

FALSE

When using a linear programming model to solve the diet problem, the objective is generally to maximize nutritional content. True or False

FALSE

When using a linear programming model to solve the diet problem, the objective is generally to maximize profit. True or False

FALSE

A mixed integer program has only integers as a solution they are simply mixed, as opposed to an integer program where they are specific to the decision variables. True or False

False

If we are solving a 0-1 integer programming problem, the constraint x1 = x2 is a conditional constraint.

False

In a mixed integer model, the solution values of the decision variables are 0 or 1.

False

In the classic game show Password, the suave, silver-haired host informed the contestants, "you can choose to pass or to play." This expression suggests a mixed integer model is most appropriate.

False

Rounding non-integer solution values up to the nearest integer value will result in an infeasible solution to an integer linear programming problem.

False

is not part of a Monte Carlo simulation

Finding an optimal solution

For every $1 increase in the budget, the ad campaign can reach twelve more customers.

The following is a graph of a linear programming problem. The feasible solution space is shaded, and the optimal solution is at the point labeled Z*. Which of the following points is not feasible?

A horse and two llamas are discussing the key areas of their domain on a lazy summer afternoon. The llamas favor the pond and shade and like to browse the fruit trees and oaks on the property, making their way to the barn only when their owner favors them with some oats. The horse prefers to graze the grass and hay for food and drink from the pond but will race up to the barn when the owner is handing out oats up there. Between the three of them, they have stepped off the distances between many of these key points several times and believe that they have developed an accurate map, shown below. As incredible as it may seem, neither the horse nor the llamas have had any training in management science, which is where you come in. Which of these routes for the horse is actually the shortest between the pair of nodes?

Grass - Pond = 190'

Betz Company manufactures ignorance in a southwestern factory and delivers it to cities in a 150-mile radius. The network diagram given in the figure below shows the possible routes and travel times (in hours) from the plant to the cities that are in the market for ignorance. (picture/figure in document) G = Guymon, W = Woodward, L = Lawton, E = Edmond, N = Norman, A = Ardmore, M = Muskogee 91) Determine the shortest route for a delivery truck from the plant in Guymon to customers in Ardmore, Edmond, and Muskogee State the total completion time in hours for each route.

Guymon-Woodward-Ardmore: 10 + 9 = 19 Guymon-Woodward-Edmond: 10 + 10 = 20 Guymon-Woodward-Edmond-Muskogee: 10 + 10 + 8 = 28

The college director of global activities was hopeful that the print ads in the school newspaper and 30 second spots on the campus radio station would spur some interest in the array of study tour and study abroad options he had secured. The communications director for the college had other ideas; she favored a social media campaign consisting of tweets and facebook postings. "This is the most ridiculous thing I ever heard of," he whined to the dean. The communications director's market research revealed the following: The advertising budget is $3500, but there is no requirement that all the money be spent. The newspaper has only four issues before the end of the semester, but the radio is a 24/7 operation and has two dozen 30 second slots available. Facebook postings must be alternated with the rest of the mindless drivel posted on the college page; thus there is space for only three postings before the end of the semester. Twitter is complicated by the 140 character requirement. The communications director feels she needs five tweets to convey a single message about tours and semesters abroad, so for one message, the cost would be $25 for each of the five components of the single ad. Due to thumb fatigue, she feels that she has only 2800 characters left in her thumbs before the end of the semester. (A side note - During the intersession period, she plans to embark on a strict regimen of thumb yoga to prepare for the coming semester.) How should the entry for the Newspaper decision variable be interpreted?

If the director were forced to purchase a newspaper advertisement, he would reach 1000 fewer customers than would be reached using the optimal advertising campaign

Use the scheme of location (J, C, or G) and excursion (S, P, H, L, Te or Tu) to represent the decision variables. What of these sets of constraints appropriately limits the number of excursions based on the scenario?

JS + JP + JH + JL = 1 CS + CP + CH + CL + CTe = 1 GS + GP + GH + GL + GTu = 1

86) If the optimal assignments include raking to Dolly, cooking to PJ, and mucking to Billy, what tasks are assigned to Jeffy and Thel?

Jeffy is assigned to the slaughter task and Thel receives the plucking task

Zevon Enterprises Zevon Enterprises provides services for clients worldwide and to protect all parties to this course as well as Zevon, we shall refer to those services as X1, X2, and X3. Each of these services has its own special mix of needs for the resources the company has at its disposal. The X1 product requires three lawyers, seven guns, and $6,000; the X2 product requires two lawyers, five guns, and $4,000; and the X3 product requires four lawyers, six guns, and $7,000. Zevon has access to 5,000 lawyers, 10,000 guns, and $15,000,000. For ease of conversation, Zevon employees usually speak about dollars as "per thousand" so one of them asking for $7 means that they really need $7,000. Zevon's demand is variable depending on what they charge for it. For example, the X1 product's demand is 200 - 2.25p1. The demand for X2 is 300 - 3p2, and the demand for X3 is 400 - 3.5p3. The per unit profit for X1 through X3 can be calculated by subtracting the per unit cost from the sales price, so for X1, the profit is p1 - 2.25, for X2 the profit is p2 - 3, and for X3 the profit is p3 - 3.5. 73) Formulate an appropriate objective function for this scenario.

Max Z = (p1 - 2.25)X1 + (p2 - 3)X2 + (p3 - 3.5)X3

After months of broken promises, partial payments, and general stupidity, the landlord had no choice but to evict the long term tenants that had become little more than squatters in his first rental property. As he surveyed the damage and pondered a mix of repairs an upgrades, he scoured the latest statistics on what different upgrades might be worth in terms of increased rent. Beautifully refinished wood floors could increase the monthly rent about $100 and an upgrade to the kitchen would fetch $80 per month. The garage door needed replacement, but even though it would receive daily use, it was almost an order qualifier, and wouldn't net more than $20 per month. The house had always suffered from lack of a back door&8211;you had to access the backyard through the garage, so taking out a window and replacing it with a safety door would cost $250 and add only $15 to the monthly rent. The garage door would cost $350, the kitchen update would cost $1000 if he went with granite, and the floor refinish job would cost $400 to rent the buffer and buy the chemicals. It wouldn't be easy doing these upgrades; the garage door would take a half week, the back door one week, the floors two weeks and the tile three weeks. There was another way around these jobs though; instead of doing them himself, the landlord could always hire a professional in each field that could finish the job in half the time but would charge a pretty penny for that speed. Refinishing floors would cost $2700, upgrading the kitchen would cost $2500, replacing the back window with a door would cost $600, and installing a garage door opener would cost $350. The landlord uses the following scheme for decision variables: What should the objective function be?

Max Z = 100x1 + 100x2 + 80x3 + 80x4 + 15x5 + 15x6 + 20x7 + 20x8

Max Z = 1500 Bar + 5000 Food + 17000 Excursion

Their cruise would port out of New Orleans and promised seven days with a panoply of excursions in Jamaica, Cozumel, and Grand Cayman. A list of excursions at each site and key features of each appear in the table. The excursions were all day affairs, so it was possible to engage in only one per port. The cruise ship sailed at night and docked at each of these three ports at the crack of dawn. By dinner time, the ship was on its way to the next port and next set of excursions. The couple was energetic and active for a pair of 52 year-olds., and while enjoying an upper middle class lifestyle, they didn't want to spend money on excursions that might be better spent on tacky souvenirs. The couple therefore budgeted $250 for the excursions&8211;the prices shown are per couple, so for example, the $60 will pay for both of them to fill up on jerk chicken and mannish water. For each of the duplicate excursions (e.g., snorkeling is offered in all three ports), the couple researched the quality of the activity and ranked the excursion among the available alternatives, with higher numbers indicating better quality. Thus, snorkeling in Jamaica is better than in Cozumel, and snorkeling in Cozumel is better than in Grand Cayman. For the unique experiences, i.e., the turtle farm, the default rating was the a 3. (Note - data used in this test question should not be construed as vacation advice.) What is an appropriate objective function for this vacation?

Max Z = 3JS + 1JP + 2JH + 3JL + 2CS + 3CP + 1CH + 2CL + 3CTe + 1GS + 2GP + 3GH + 1GL + 3GTu

What is an appropriate objective function for this vacation? Max Z = 3JS + 1JP + 2JH + 3JL + 2CS + 3CP + 1CH + 2CL + 3CTe + 1GS + 2GP + 3GH + 1GL + 3GTu Max Z = JS + JP + JH + JL + CS + CP + CH + CL + CTe + GS + GP + GH + GL + GTu Min Z = 100JS + 95JP + 120JH + 60JL + 110CS + 55CP + 70CH + 90CL + 130CTe + 90GS + 60GP + 110GH + 130GL + 95GTu Min Z = 3JS + 1JP + 2JH + 3JL + 2CS + 3CP + 1CH + 2CL + 3CTe + 1GS + 2GP + 3GH + 1GL + 3GTu

Max Z = 3JS + 1JP + 2JH + 3JL + 2CS + 3CP + 1CH + 2CL + 3CTe + 1GS + 2GP + 3GH + 1GL + 3GTu

The college director of global activities was hopeful that the print ads in the school newspaper and 30 second spots on the campus radio station would spur some interest in the array of study tour and study abroad options he had secured. The communications director for the college had other ideas; she favored a social media campaign consisting of tweets and facebook postings. "This is the most ridiculous thing I ever heard of," he whined to the dean. The communications director's market research revealed the following: The advertising budget is $3500, but there is no requirement that all the money be spent. The newspaper has only four issues before the end of the semester, but the radio is a 24/7 operation and has two dozen 30 second slots available. Facebook postings must be alternated with the rest of the mindless drivel posted on the college page; thus there is space for only three postings before the end of the semester. Twitter is complicated by the 140 character requirement. The communications director feels she needs five tweets to convey a single message about tours and semesters abroad, so for one message, the cost would be $25 for each of the five components of the single ad. Due to thumb fatigue, she feels that she has only 2800 characters left in her thumbs before the end of the semester. (A side note - During the intersession period, she plans to embark on a strict regimen of thumb yoga to prepare for the coming semester.) What is an appropriate objective function for this scenario?

Max Z = 5,000N + 3,000R + 700T + 200F

115) What is the complete linear model for this scenario?

Min Z = $3AD + $3AE + $4BD + $3BE + $5CD + $3CE + $4DF + $4DG + $4DH + $10EF + $9EG + $8EH AD + AE = 200 BD + BE = 300 CD + CE = 500 DF + EF = 350 DG + EG = 450 EF + EH = 200 AD + BD + CD - DF - DG - DH = 0 AE + BE + CE - EF - EG - EH = 0 AD + BD + CD ≤ 600 AE + BE + CE ≤ 700

In all the excitement of waving to the longshoremen as the ship leaves the Port of New Orleans, the management scientist drops his wallet in the Mississippi River. Rather than maximize enjoyment for the three excursions, he must now adjust his model to select three inexpensive options. Which combinations of objective function and constraints are best if the scheme of location (J, C, or G) and excursion (S, P, H, L, Te or Tu) is used to represent the decision variables?

Min Z = 100JS + 95JP + 120JH + 60JL + 110CS + 55CP + 70CH + 90CL + 130CTe + 90GS + 60GP + 110GH + 130GL + 95GTu subject to: JS + JP + JH + JL = 1 CS + CP + CH + CL + CTe = 1 GS + GP + GH + GL + GTu = 1

In a ________ linear programming model, some of the solution values for the decision variables are required to assume integer values and others can be integer or noninteger.

Mixed Integer

________ involves determining the functional relationship between variables, parameters, and equations.

Model construction

87) What are the linear programming constraints for mucking and Thel?

Mucking: XMB + XMD + XMJ + XMP+ XMT = 1 Thel: XRT + XCT + XMT + XPT+ XST = 1

91) The committee would like to assign three reviewers to each applicant. A partial solution to this problem is shown below, where the number 1 indicates when a reviewer is assigned to an applicant. Assign reviewers to Applicant B and Applicant C. (BETTER CHART IN DOCUMENT) Applicant Reviewer A B C 1 X 2 X 3 1 X 4 1 5 X 6 X 7 X 8 X 9 1 X

Multiple optimal solutions Applicant Reviewer A B C 1 0 0 1 2 0 1 0 3 1 0 0 4 1 0 0 5 0 1 0 6 0 0 1 7 0 0 1 8 0 1 0 9 1 0 0 Assigned 3 3 3 Applicant Reviewer A B C 1 1 0 0 2 0 1 0 3 1 0 0 4 0 0 1 5 0 1 0 6 1 0 0 7 0 0 1 8 0 1 0 9 0 0 1 Assigned 3 3 3

The production manager for the Coory soft drink company is considering the production of two kinds of soft drinks: regular and diet. Two of her limited resources are production time (8 hours = 480 minutes per day) and syrup (1 of the ingredients), limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case. What are the optimal daily production quantities of each product and the optimal daily profit?

R = 90, D = 75, Z = $420

The department chair reviewed last year's schedule, the degree requirements for the ever popular Operations and Supply Chain major, and the emails that had drifted into her mailbox over the last week. Naturally, every professor in the department had his own pet course and wanted to maintain control of it while avoiding 8 a.m. classes at all costs. In an effort to placate the senior faculty members of the department, the chair sent an email asking them to supply the prep time for each of the classes they were qualified to teach, promising to assign them the least taxing schedule possible. Each of her department members had to teach at least two courses, but no more than three. The elective courses, Project Management, Quality Management, Control and Planning, Logistics, and Management Science each had to be offered once and the department needed to offer at least six sections of the Introduction to Operations class. The prep times each professor estimated for each course appear in the table below. Which constraint ensures that Introduction to Operations is offered according to the scenario?

SI + GI + TI + DI ≥ 6

SI + SP + SQ + SC + SL + SM ≤ 3

T/F: If we are solving a 0-1 integer programming problem, the constraint x1 + x2 ≤ 1 is a mutually exclusive constraint.

T/F: If we are solving a 0-1 integer programming problem, the constraint x1 ≤ x2 is a conditional constraint.

10) The minimal spanning tree problem is to connect all nodes in a network so that the total branch lengths are minimized.

TRUE

11) The transshipment model includes intermediate points between the sources and destinations.

TRUE

12) Both linear and nonlinear programming models are examples of constrained optimization models.

TRUE

12) In a transshipment problem, items may be transported from sources through transshipment points on to destinations.

TRUE

12) The last step of the minimal spanning tree solution method is to make sure all nodes have joined the spanning tree.

TRUE

13) In a transshipment problem, items may be transported from one source to another.

TRUE

14) In a transshipment problem, items may be transported from one transshipment point to another.

TRUE

14) The Lagrange multiplier is analogous to the dual variables in a linear programming problem.

TRUE

15) In a transshipment problem, items may be transported from one destination to another.

TRUE

15) The Lagrange multiplier at the optimum gives only the instantaneous rate of change in the objective value.

TRUE

16) In a transshipment problem, items may be transported directly from sources to destinations.

TRUE

17) Classical optimization is the use of calculus to determine the optimal value of a variable.

TRUE

17) In a transshipment problem, items may be transported from destination to destination and from source to source.

TRUE

17) Regardless of the number of nodes in a network, the minimal spanning tree always contains the two nodes with the shortest distance between them.

TRUE

18) An assignment problem is a special form of transportation problem where all supply and demand values equal 1.

TRUE

19) Assignment linear programs always result in integer solutions.

TRUE

19) In an unconstrained nonlinear programming problem, we have a single nonlinear objective function and no constraints.

TRUE

23) The maximal flow solution algorithm allows the user to choose a path through the network from the origin to the destination by any criteria.

TRUE

24) A traffic system could be represented as a network in order to determine bottlenecks using the maximal flow network algorithm.

TRUE

3) Branches connect nodes and show flow from one point to another.

TRUE

3) The highest point on each peak of a surface can be considered a local optimum, but the highest point among all of the peaks is the only global optimum.

TRUE

3) The linear programming model for a transportation problem has constraints for supply at each source and demand at each destination.

TRUE

6) The shortest route problem is to find the shortest distance between an origin and various destination points.

TRUE

7) Classical optimization uses calculus to determine the optimal values of a variable.

TRUE

7) Once the shortest route to a particular node has been determined, that node becomes part of the permanent set.

TRUE

9) A prohibited route in a transportation model should be assigned an arbitrarily high cost coefficient.

TRUE

9) The shortest route network problem could help identify the best route for pizza delivery drivers from the pizza parlor to a specific customer.

TRUE

A company can use regular time, overtime, and subcontracting in any amount over the one-year production planning horizon to meet forecasted demand. If they develop the plan using linear programming, they will have a total of 36 decision variables that govern the amount produced by these three methods. True or False

TRUE

A feasible solution to an integer programming problem is ensured by rounding down non-integer solution values. True or False

TRUE

Blending problems usually require algebraic manipulation in order to write the LP in "standard form." True or False

TRUE

Determining the production quantities of different products manufactured by a company based on resource constraints is a product mix linear programming problem. True or False

TRUE

If we are solving a 0-1 integer programming problem, the constraint x1 + x2 ≤ 1 is a mutually exclusive constraint. True or False

TRUE

If we are solving a 0-1 integer programming problem, the constraint x1 ≤ x2 is a conditional constraint. True or False

TRUE

In a 0-1 integer model, the solution values of the decision variables are 0 or 1. True or False

TRUE

In a balanced transportation model, supply equals demand such that all constraints can be treated as equalities. True or False

TRUE

In a media selection problem, instead of having an objective of maximizing profit or minimizing cost, generally, the objective is to maximize the audience exposure. True or False

TRUE

In a mixed integer model, some solution values for decision variables are integer and others can be non-integer. True False

TRUE

In a problem involving capital budgeting applications, the 0-1 variables designate the acceptance or rejection of the different projects. True or False

TRUE

In a total integer model, all decision variables have integer solution values. True or False

TRUE

In a transportation problem, a demand constraint for a specific destination represents the amount of product demanded by a given destination (customer, retail outlet, store). True or False

TRUE

In a transportation problem, the supply constraint represents the maximum amount of product available for shipment or distribution at a given source (plant, warehouse, mill). True or False

TRUE

Integer constraints are entered in the inequality dialog box within Excel's Solver routine. True or False

TRUE

One type of constraint in an integer program is a multiple-choice constraint. True or False

TRUE

Rounding non-integer solution values up to the nearest integer value can result in an infeasible solution to an integer programming problem. True or False

TRUE

The feasible region in an integer programming graph is composed of a lattice of points. True or False

TRUE

The production planner for Airbus showed his boss the latest product mix suggestion from their slick new linear programming model: 12.5 model 320s and 17.4 model 340s. The boss looked over his glasses at the production planner and reminded him that they had several unsold half airplanes from last year's production rusting in the parking lot. No one, it seems, is interested in half of an airplane. The production planner whipped out his red pen and crossed out the .5 and .4, turning the new plan into 12 model 320s and 17 model 340s. This production plan is definitely feasible. True or False

TRUE

123) Consider the network shown in the figure. The architect decides to remove a few of the (undirected) arcs but still have each node connected to at least one other node within a single network. Which arcs should be removed and what is the total arc length that is removed?

The arcs to be removed are arcs 1 - 2 = 13, 2 - 5 = 17, 3 - 6 = 10, 1 - 4 = 15, for a total arc length removed of 13 + 17 + 10 + 15 = 55 units. The remaining arc length is 40. Not too shabby!

105) The horse isn't crazy about it, but occasionally will relent and pull a cart laden with supplies from the barn to the other points of mutual interest, the grassy area, the pond, and the hay down in the run in shed. What is the shortest distance from the barn to each of these points?

The distance and route from the barn are given in this table: (better chart in the document) From the Barn to Distance Route Grass 70' direct Hay 140' Oak-Hay Pond 170' Oak-Pond

Comedy Pasture II A horse and two llamas are discussing the key areas of their domain on a lazy summer afternoon. The llamas favor the pond and shade and like to browse the fruit trees and oaks on the property, making their way to the barn only when their owner favors them with some oats. The horse prefers to graze the grass and hay for food and drink from the pond but will race up to the barn when the owner is handing out oats up there. Between the three of them, they have stepped off the distances between many of these key points several times and believe that they have developed an accurate map, shown below. This map shows the number of loads that can be hauled between all connected points on the property. As incredible as it may seem, neither the horse nor the llamas have had any training in management science, which is where you come in. (FIGURE) 108) The horse spoke up first, "I'm twice your size and can work twice as hard. It doesn't matter how much needs to be hauled from the grassy area in the comedy pasture down to the pond, I can do it easily in a day." Of course, the horse would use only routes connected by his nodes of interest, Grass, Barn, Oak, Hay and Pond. Use the capacities indicated on each of the branches to determine the maximal flow down to the pond.

The maximum flow is 14 using these paths: Grass-Hay = 6, continuing on Hay-Pond Grass-Oak = 8, continuing on Oak-Pond

109) The llamas took pride in the centuries old use as pack animals in the South American Andes. Using only their network of nodes, Fruit, Barn, Grass, Oak, Shade, Hay and Pond, they figured they could easily outhaul the horse. Use the capacities indicated on each of the branches to determine the maximal flow from the Barn down to the pond.

The maximum flow is 20 using these paths: Barn - Oak - Pond = 8 Barn - Oak - Hay - Pond = 2 Barn - Shade - Oak - Fruit - Pond = 5 Barn - Fruit Oak - Shade - Hay - Pond = 5

111) The llamas took pride in the centuries old use as pack animals in the South American Andes. They decided to join forces with their grazing buddy the horse and lug hay from the Barn down to the area designated as Hay for long term storage. Use the capacities indicated on each of the branches to determine the maximal flow from the Barn down to Hay.

The maximum flow is 20 using these paths: Barn-Grass-Hay = 7 Barn-Oak-Hay = 6 Barn-Fruit-Oak-Shade-Hay = 5

110) The llamas took pride in the centuries old use as pack animals in the South American Andes. They decided to join forces with their grazing buddy the horse and lug ripe fruit from the orchard (designated as Fruit) down to the Pond. Use the capacities indicated on each of the branches to determine the maximal flow from the orchard down to the pond.

The maximum flow is 23 using these paths: Fruit-Pond = 5 Fruit-Barn-Grass-Oak-Pond = 8 Fruit-Oak-Grass-Hay-Pond = 7 Fruit-Barn-Oak-Shade-Hay-Pond = 3

77) The model was entered into an Excel spreadsheet and the table below shows part of the sensitivity report. Provide an interpretation. (better chart in the document) Constraints Cell Name Final Value Lagrange Multiplier $F$8 Lawyers 1358.906273 0 $F$9 Guns 2573.031361 0 $F$10 Money 2523.937562 0

The model provides a solution that calls for only 1358.9 lawyers, 2573.03 guns and 2523.9 thousands of dollars, far below the amount on hand for this endeavor. The Lagrange Multipliers are all zero, which reflects the lack of urgency in acquiring more lawyers, guns, and money. Since Zevon is not using all that they already have, there is no benefit to acquiring any more of these resources.

79) The model was entered into an Excel spreadsheet and the table below shows part of the answer report. Provide an interpretation.(better chart in the document) Constraints Cell Name Cell Value Formula Status Slack $F$8 Lawyers 1358.906273 $F$8<=$I$8 Not Binding 3641.093727 $F$9 Guns 2573.031361 $F$9<=$I$9 Not Binding 7426.968639 $F$10 Money 2523.937562 $F$10<=$I$10 Not Binding 12476.06244

The model provides a solution that calls for only 1359 lawyers out of the 5000 available, meaning Zevon has 3641 lawyers that are not assigned to this model. Similarly, only 2573 guns and $2,523,973.56 are needed out of the 10,000 guns and $15,000,000 available to them.

Mad Over Donuts An entrepreneurial resident of the Oklahoma City metropolitan area is interested in securing a new franchise for Mad Over Donuts. Ideally this franchise would be centrally located so delivery could be economically handled and all citizens could enjoy fresh, delicious donuts delivered to the doorstep. The main cities and anticipated demand (in thousands per day) are shown in the table. (better chart in the document) City x-coord y-coord Demand Jones 6 28 45 Luther 13 35 56 Harrah 12 22 30 Edmond 0 32 25 Norman 2 0 33 Moore 3 8 22 82) What is the appropriate objective function for this scenario?

The objective function is: (he has weird equations for z and d and they won't copy and paste correctly so you'll have to look at the document for that) Min Z = where d = and ti = the number of trips (demand)

81) The analytics gurus at Zevon realize that they had misformulated their demand curves. They now believe that demand for X1 is given by 1000 - 2.25p1, demand for X2 is given by 2000 - 3p2, and demand for X3 is given by 3000 - 3.5p3. This model is entered in Excel and the sensitivity report contains the following: (better chart in the document) Constraints Cell Name Final Value Lagrange Multiplier $F$8 Lawyers 5000.00 101.052 $F$9 Guns 9275.74 0 $F$10 Money 9213.49 0 Provide an interpretation of all elements.

The only resource that Zevon could use more of is lawyers; the final value is 5000, which exhausts their entire supply. If additional lawyers could be retained for less than $101.05, then Zevon should pursue this possibility. There is no information available as to the range for the validity of this $101.05. The guns resource has only 725 units remaining and the money resource has $5,800 left. When one of those two resources is exhausted, the lawyer Lagrange multiplier will likely not be valid.

After months of broken promises, partial payments, and general stupidity, the landlord had no choice but to evict the long term tenants that had become little more than squatters in his first rental property. As he surveyed the damage and pondered a mix of repairs an upgrades, he scoured the latest statistics on what different upgrades might be worth in terms of increased rent. Beautifully refinished wood floors could increase the monthly rent about $100 and an upgrade to the kitchen would fetch $80 per month. The garage door needed replacement, but even though it would receive daily use, it was almost an order qualifier, and wouldn't net more than $20 per month. The house had always suffered from lack of a back door&8211;you had to access the backyard through the garage, so taking out a window and replacing it with a safety door would cost $250 and add only $15 to the monthly rent. The garage door would cost $350, the kitchen update would cost $1000 if he went with granite, and the floor refinish job would cost $400 to rent the buffer and buy the chemicals. It wouldn't be easy doing these upgrades; the garage door would take a half week, the back door one week, the floors two weeks and the tile three weeks. There was another way around these jobs though; instead of doing them himself, the landlord could always hire a professional in each field that could finish the job in half the time but would charge a pretty penny for that speed. Refinishing floors would cost $2700, upgrading the kitchen would cost $2500, replacing the back window with a door would cost $600, and installing a garage door opener would cost $350. The landlord ran the model in Excel and received the answer report contained in the table. Which of the following statements is correct?

The rent will be $180 higher and the project will take 3.5 weeks to finish at a cost of $2900.

113) What special case of linear programming should be used to model this situation?

The scenario gives the appearance that it is an assignment model waiting to happen up until the point that six sections of Introduction to Operations are needed and the professors are responsible for two to three sections each. The easiest way to model this is by declaring it a transportation model with the six sections of Introduction to Operations as traveling to the same destination. However, if each of those six sections is a node unto itself, and if each professor is separated into three possible sources of teaching, then this would fit the assignment model. The problem with solving the scenario with an assignment model is that the number of decision variables increases from 24 to 132 and the constraints increase from 10 to 23.

83) What are the appropriate constraints for this scenario?

There are no constraints for this model. It is a nonlinear unconstrained optimization problem.

The department chair reviewed last year's schedule, the degree requirements for the ever popular Operations and Supply Chain major, and the emails that had drifted into her mailbox over the last week. Naturally, every professor in the department had his own pet course and wanted to maintain control of it while avoiding 8 a.m. classes at all costs. In an effort to placate the senior faculty members of the department, the chair sent an email asking them to supply the prep time for each of the classes they were qualified to teach, promising to assign them the least taxing schedule possible. Each of her department members had to teach at least two courses, but no more than three. The elective courses, Project Management, Quality Management, Control and Planning, Logistics, and Management Science each had to be offered once and the department needed to offer at least six sections of the Introduction to Operations class. The prep times each professor estimated for each course appear in the table below. Copied below is a portion of the answer report that shows the constraints related to the faculty assignment. Which of these statements is best according to the answer report?

Tim is assigned to teach two courses

Rounding non-integer solution values up to the nearest integer value can result in an infeasible solution to an integer programming problem.

True

The divisibility assumption is violated by integer programming

True

The production planner for Airbus showed his boss the latest product mix suggestion from their slick new linear programming model: 12.5 model 320s and 17.4 model 340s. The boss looked over his glasses at the production planner and reminded him that they had several half airplanes from last year's production rusting in the parking lot. No one, it seems, is interested in half of an airplane. The production planner whipped out his red pen and crossed out the .5 and .4, turning the new plan into 12 model 320s and 17 model 340s. This production plan is definitely feasible.

True

102) Help Mondo make the best choice of outfit for each model using linear programming.

Using a Model-Outfit sequence for the decision variables yields the following: Max Fabulosity = 9ZG + 9ZS + 4ZC + 4ZA + 2ZP + 3YG + 8YS + 3YC + 8YA + 9YP + 4XG + 7XS + 3XC + 7XA + 8XP + 1WG + 6WS + 5WC + 6WA + 9WP + 4VG + 9VS + 9VC + 6VA + 7VP Subject to: ZG + ZS + ZC + ZA + ZP = 1 YG + YS + YC + YA + YP = 1 XG + XS + XC + XA + XP = 1 WG + WS + WC + WA + WP = 1 VG + VS + VC + VA + VP = 1 ZG + YG + XG + WG + VG = 1 ZS + YS + XS +WS +VS = 1 ZC + YC + XC + WC + VC = 1 ZA + YA + XA + WA + VA = 1 ZP + YP + XP + WP + VP = 1 ZG, ZS, ZC, ZA, ZP, YG, YS, YC, YA, YP, XG, XS, XC, XA, XP, WG, WS, WC, WA, WP, VG, VS, VC, VA, VP ≥ 0

Mondo's Runway Show Mondo Guerra is matching his models with his latest collection for Fashion Week. He has five models, ranging from 5'10" to 5'10.5" and size 0 to size 1. His five latest designs run the gamut from prêt-à-porter to an evening gown and he'd like to make sure each outfit looks as good as possible by having it worn on the runway by the right model. After an anxious month of sewing, he has each model try on each outfit and he assigns a fabulosity score to each combination as indicated in the table. (BETTER CHART IN DOCUMENT) Gown Sport Couture Avant Garde Prêt-à-Porter Zoe 9 9 4 4 2 Yvette 3 8 3 8 9 Xena 4 7 3 7 8 Whisper 1 6 5 6 9 Vajay 4 9 9 6 7 100) What is an appropriate objective function for this scenario?

Using a Model-Outfit sequence for the decision variables yields the following: Max Fabulosity = 9ZG + 9ZS + 4ZC + 4ZZA + 2ZP + 3YG + 8YS + 3YC + 8YA + 9YP + 4XG + 7XS + 3XC + 7XA + 8XP + 1WG + 6WS + 5WC + 6WA + 9WP + 4VG + 9VS + 9VC + 6VA + 7VP

112) The department chair looks at past course evaluations and realizes that if she wants to attract students to the Operations and Supply Chain major, it would be best if Geoff were never assigned to teach that class. How can her standard model be modified to ensure that Geoff cannot scare away students from the major?

Using the scheme Professor:Subject for decision variables, e.g. SI is Saba teaches Intro to Ops, these additions should be made to the base model. SI + TI + DI ≥ 6 GI = 0 The difference between this model and the base is that this assigns Geoff to no sections of Introduction to Operations, while maintaining he number of sections at six or greater among the other three faculty members. This model's objective is still to minimize the number of prep hours. As luck would have it, this model performs as well as the base model, which didn't have any sections of Intro assigned to Geoff.

110) Take note of the phrase in the scenario that reads "Naturally, every professor in the department had his own pet course..." Provide an example of a constraint that makes sure a professor gets to teach his favorite course.

Using the scheme Professor:Subject for decision variables, e.g. SI is Saba teaches Intro to Ops, we can ensure that Saba is assigned to Intro to Operations by entering the constraint: SI ≥ 2 along with the other constraints in the model. If Geoff likes Logistics, then GL = 1 would assign that professor the logistics class.

109) Write the model that is suitable for this scenario.

Using the scheme Professor:Subject for decision variables, e.g. SI is Saba teaches Intro to Ops: Min Z = 3SI + 10SP + 12SQ + 16SC + 12SL + 7SM + 4GI + 19GP + 2GQ + 10GC + 8GL + 18GM + 5TI + 11TP + 4TQ + 14TC + 14TL + 3TM + 4DI + 11DP + 4DQ + 15DC + 17DL + 15DM SI + SP + SQ + SC + SL + SM ≤ 3 SI + SP + SQ + SC + SL + SM ≥ 2 GI + GP + GQ + GC + GL + GM ≤ 3 GI + GP + GQ + GC + GL + GM ≥ 2 TI + TP + TQ + TC + TL + TM ≤ 3 TI + TP + TQ + TC + TL + TM ≥ 2 DI + DP + DQ + DC + DL + DM ≤ 3 DI + DP + DQ + DC + DL + DM ≥ 2 SI + GI + TI + DI ≥ 6 SP + GP + TP + DP = 1 SQ + GQ + TQ+ DQ = 1 SC + GC + TC + DC = 1 SL + GL + TL+ DL = 1 SM + GM + TM + DM = 1

Due to increased sales, a company is considering building three new distribution centers (DCs) to serve four regional sales areas. The annual cost to operate DC 1 is $500 (in thousands of dollars). The cost to operate DC 2 is $600 (in thousands of dollars). The cost to operate DC 3 is $525 (in thousands of dollars). Assume that the variable cost of operating at each location is the same, and therefore not a consideration in making the location decision. The table below shows the cost ($ per item) for shipping from each DC to each region. The demand for region A is 70,000 units; for region B, 100,000 units; for region C, 50,000 units; and for region D, 80,000 units. Assume that the minimum capacity for the distribution center will be 500,000 units. Assume that Xij = quantity shipped from distribution i to region j. i = 1,2,3 and j = 1, 2, 3, 4. Assume that Yi = 0 or 1 where i = distribution center 1, 2 or 3. The constraint for distribution center 1 is:

X11 + X12 + X13 + X14 - 500y1 ≤ 0

The constraint for the South Asia demand region is:

X13 + X23 + X33 + X43 = 7.

96) What is the constraint for the transshipment node in Philadelphia for the Mantastic problem?

X13 + X23 + X43 — X34 - X35 - X36 - X37 = 0

In setting up the an intermediate (transshipment) node constraint, assume that there are three sources, two intermediate nodes, and two destinations, and travel is possible between all sources and the intermediate nodes and between all intermediate nodes and all destinations for a given transshipment problem. In addition, assume that no travel is possible between source nodes, between intermediate nodes, and between destination nodes, and no direct travel from source nodes to destination nodes. Let the source nodes be labeled as 1, 2, 3, the intermediate nodes be labeled as 4 and 5, and the destination nodes be labeled as 6 and 7. 92) State the constraint for intermediate node 4.

X14 + X24 + X34 - X46 - X47 = 0

89) Awards committees need to be formed to review potential award recipients. In the past, three people have been assigned to review each applicant. The only stipulation is that a reviewer cannot be assigned to an applicant if the applicant is a co-worker. The matrix below shows 9 reviewers, 3 candidates, and a matrix. If an entry in the matrix contains an "X," then that specific reviewer is ineligible to review an applicant's material. For example, reviewer 1 cannot review materials submitted by candidate B. It is possible that some reviewers may not receive an assignment. (BETTER CHART IN DOCUMENT) Applicant Reviewer A B C 1 X 2 X 3 X 4 5 X 6 X 7 X 8 X 9 X Formulate this as an assignment problem in which two reviewers are assigned to review each applicant's material.

X1A + X1B + X1C ≤ 1 X2A + X2B + X2C ≤ 1 X3A + X3B + X3C ≤ 1 X4A + X4B + X4C ≤ 1 X5A + X5B + X5C ≤ 1 X6A + X6B + X6C ≤ 1 X7A + X7B + X7C ≤ 1 X8A + X8B + X8C ≤ 1 X9A + X9B + X9C ≤ 1 X1A + X3A + X4A + X6A + X7A + X8A + X9A = 2 X2B + X3B + X4B + X5B + X8B = 2 X1C + X2C + X4C + X5C + X6C + X7C + X9C = 2

116) Consider the network diagram given in Figure 3 with the indicated flow capacities along each branch. What is the input-output constraint associated with the ninth node of the network diagram for the 0-1 integer linear programming formulation of the maximal flow problem?

X79 + X89 - X91 = 0

117) Consider the network diagram given in Figure 3 with the indicated flow capacities along each branch. What is the capacity constraint associated with the branch from node 7 to node 9 of the network diagram for the 0-1 integer linear programming formulation of the maximal flow problem?

X79 ≤ 8

115) Consider the network diagram given in Figure 3 with the indicated flow capacities along each branch. What is the input- output constraint associated with the first node of the network diagram for the 0-1 integer linear programming formulation of the maximal flow problem?

X91 - X12 - X13 - X14 = 0

94) Write the constraint associated with the Muskogee (destination) node for the 0-1 integer linear programming formulation of the shortest route problem.

XEM + XNM + XAM = 1

93) Write the constraint associated with the Guymon (source) node for the 0-1 integer linear programming formulation of the shortest route problem.

XGW + XGL = 1

Joe Jackson runs the ABC123 manufacturing company that produces hit records. The annual fixed cost is $2,000 and the variable cost per recording $8. The price is related to demand according to the following equation: 200 - 2.5p. 65) What is the nonlinear profit function for the ABC123 company? Simplify the terms as much as possible.

Z = -2.5p2 + 220p - 3,600

Which of the following could be a linear programming objective function?

Z = 1A + 2B + 3C + 4D

104) You formulate this as an assignment model and review the Zoe section of the sensitivity analysis with Mondo. Provide him with an interpretation. (BETTER CHART IN DOCUMENT) Cell Name Final Value Reduced Cost Objective Coefficient Allowable Increase Allowable Decrease $J$13 Zoe Gown 1 0 9 1E+30 3 $K$13 Zoe Sport 0 0 9 3 2 $L$13 Zoe Leisure 0 -2 4 2 1E+30 $M$13 Zoe Cocktail 0 -5 4 5 1E+30 $N$13 Zoe Pret a Porter 0 -8 2 8 1E+30

Zoe is assigned to wear the gown and will add 9 points to the overall fabulosity score. Even if Zoe's rating in the gown was up to 3 points lower, she would still be assigned to wear the gown. The overall score would be lower, but this would still be her assignment. Normally, the reduced cost entries speak to the change in objective coefficients before the assignment changes. As the model was presented, the coefficient for Zoe in the Leisure outfit was 4, with a reduced cost of -2, so a change in excess of 4 to 4- -2 = 6 would cause the Leisure outfit assignment to be optimal. As this is a balanced model, we cannot make that statement.

30) A plant has four jobs to be assigned to four machines, and each machine has different manufacturing times for each product. The production manager wants to determine the optimal assignments of four jobs to four machines to minimize total manufacturing time. This problem can be most efficiently solved using the ________ model.

assignment

In a single-server queuing model, L represents the

average number of customers waiting and being served

Aunt Anastasia operates a small business: she produces seasonal ceramic objects to sell to tourists. For the spring, she is planning to make baskets, eggs, and rabbits. Based on your discussion with your aunt you construct the following table: Your aunt also has committed to make 25 rabbits for a charitable organization. Based on the information in the table, you formulate the problem as a linear program. MAX 2.5B + 1.5E + 2R s.t. The Excel solution and the answer and sensitivity report are shown below. The Answer Report: The Sensitivity Report: Aunt Anastasia is planning for next spring, and she is considering making only two products. Based on the results from the linear program, which two products would you recommend that she make?

baskets and rabbits

Taco Loco is considering a new addition to their menu. They have test marketed a number of possibilities and narrowed them down to three new products, X, Y, and Z. Each of these products is made from a different combination of beef, beans, and cheese, and each product has a price point. Taco Loco feels they can sell an X for $17, a Y for $13, and a Z for $14. The company's management science consultant formulates the following linear programming model for company management. The sensitivity report from the computer model reads as follows: The local cheese vendor offers to sell Taco Loco 200 pounds of cheese for these three products. Taco Loco should:

buy 46 pounds or less of cheese for $1.45 or less.

The field of management science:

concentrates on the use of quantitative methods to assist managers in decision making.

If we are solving a 0-1 integer programming problem, the constraint x1 ≤ x2 is a ________ constraint. multiple choice mutually exclusive conditional corequisite

conditional

31) In a linear programming formulation of a transportation model, each of the possible combinations of supply and demand locations is a(n) ________.

decision variable

If the price increases, but fixed and variable costs do not change, the break-even point

decreases.

In a balanced transportation model, supply equals ________.

demand

Coefficient of determination is the percentage of the variation in the ________ variable that results from the ________ variable

dependent, independent

Cranky Jerry's Day Care wants to minimize their food cost while meeting the minimum (and I mean bare minimum) guidelines for nutrition as set forth by the state. The best approach would be to follow the example in this chapter for a(n) ________ problem.

diet

Rounding a noninteger solution ________ to the nearest integer guarantees a feasible, but perhaps suboptimal solution to an integer programming situation.

down

Data envelopment analysis indicates the relative ________ of a service unit compared with others.

efficiency or productivity

In a transshipment problem, items may be transported:

from destination to destination. from one transshipment point to another. directly from sources to destinations. Correct All of these

If we wanted to represent an office layout as a network flow problem, which of the following would be represented as a branch?

heating and ventilation systems

25) In order to model a "prohibited route" in a transportation or transshipment problem, the cost assigned to the route should be ________.

high

If fixed costs increase, but variable cost and price remain the same, the break-even point:

increases

If the price decreases, but fixed and variable costs do not change, the break-even point:

increases.

In a network flow model, a directed branch

is a branch in which flow is possible in only one direction.

A slack variable:

is the amount by which the left side of a ≤ constraint is smaller than the right side.

37) In a typical network flow problem, the branches show flow from one node to the next. The nodes themselves are ________ points.

junction (connecting)

Linear mathematical programming techniques assume that all parameters in the models are:

known with certainty.

Random numbers generated by a ________ process instead of a ________ process are pseudorandom numbers

mathematical, physical

40) Determining where capacity needs to be added within a series of one-way roads within a park represents a(n) ________ model.

maximal flow

114) Consider the network diagram given in Figure 3 with the indicated flow capacities along each branch. What is the objective function for the 0-1 integer linear programming formulation of the maximal flow problem?

maximize Z = X91

Refer to the figure below to answer the following questions. Figure 3 112) Consider the network diagram given in Figure 3 with the indicated flow capacities along each branch. Determine the maximal flow from source node 1 to destination node 9.

maximum flow: 13

113) Consider the network diagram given in Figure 3 with the indicated flow capacities along each branch. Determine the maximal flow on the following path: node 1 to node 4 to node 6 to node 8 to destination node 9.

maximum flow: 4

29) The ________ connects all nodes in a network so that the total branch lengths are minimized.

minimal spanning tree

The objective function of a diet problem is usually to ________ subject to nutritional requirements.

minimize costs

A(n) ________ integer model allows for the possibility that some decision variables are not integers.

mixed

"It's me or the cat!" the exasperated husband bellowed to his well-educated wife. "Hmmmm," she thought, "I could model this decision with a ________ constraint."

mixed or mutually exclusive

In choosing four electives from the dazzling array offered by the Decision Sciences Department next semester, the students that had already taken the management science class were able to craft a model using a(n) ________ constraint.

multiple-choice

In a 0-1 integer programming model, if the constraint x1 - x2 = 0, it means when project 1 is selected, project 2 ________ be selected. must also can never can also can sometimes

must also

If we are solving a 0-1 integer programming problem, the constraint x1 + x2 ≤ 1 is a ________ constraint

mutually exclusive

In a network modeling problem, the linear programming decision variables are given by

network branches.

In a data envelopment analysis, it is customary to scale input process so that the total value of a unit's inputs equals ________.

one

87) Determine the prices that Sara should charge to maximize profit.

p1 = 7 p2 = 4

28) The shipping company manager wants to determine the best routes for the trucks to take to reach their destinations. This problem can be solved using the ________ solution technique.

shortest route

The shipping company manager wants to determine the best routes for the trucks to take to reach their destinations. This problem can be solved using the

shortest route solution technique.

38) The ________ measure of distance between two points on a set of X and Y coordinates is the hypotenuse of a right triangle.

straight line (direct, Euclidian)

If we wanted to represent an urban transportation system as a network flow problem, which of the following would be represented as nodes?

street intersections

In the linear programming formulation of a transportation network

there is one variable for each arc. there is one constraint for each node. the sum of variables corresponding to arcs out of an source node is constrained by the supply at that node. Correct All of these

There are three plants scattered across the United States that manufacture Dull computers. These plants assemble products for customers throughout the United States, Canada, and Mexico. If Dull wishes to maximize profit by choosing the most economical pair of factory and customer for each order, they would be well-advised to follow the ________ model presented in this chapter.

transportation problem

26) The ________ model is an extension of the transportation model in which intermediate points are added between the sources and destinations.

transshipment

28) An appropriate choice of a model for analyzing the best shipping routes for a supply chain consisting of a manufacturer, warehouse, and retailer would be the ________ model.

transshipment

A ________ is a gradual, long-term, up-or-down movement of demand.

trend

35) If the number of sources is greater than the number of destinations, then we have a(n) ________ assignment problem.

unbalanced

24) If a nonlinear programming model consists of a single nonlinear objective function and no constraints, it is called a(n) ________ optimization problem.

unconstrained

Rounding a noninteger solution ________ to the nearest integer value will likely result in an infeasible solution.

36) The ________ of the value of investment is a measure of risk.

variance

Use the constraints given below and determine which of the following points is feasible.

x = 1; y = 4

In an integer program, if we were choosing between two locations to build a facility, this would be written as:

x1 + x2 = 1

In an integer program, if we were choosing between two locations to build a facility, this would be written as: ________.

x1 + x2 = 1

In a capital budgeting problem, if either project 1 or project 2 is selected, then project 5 cannot be selected. Which of the alternatives listed below correctly models this situation? x1 + x2 + x5 ≤ 1 x1 - x5 ≤ 1, x2 - x5 ≤ 1 x1 + x5 ≤ 1, x2 + x5 ≤ 1 x1 + x2 + x5 ≥ 1

x1 + x5 ≤ 1, x2 + x5 ≤ 1

72) Lush Lawns, Inc. provides a lawn fertilizer and weed control service. They are adding a special aeration treatment as a low-cost extra service option, which it hopes will help attract new customers. Management is planning to promote this new service in two media: radio and direct-mail advertising. A budget of $2000 is to be used on this promotional campaign over the next quarter. Based on past experience in promoting its other services, Lush Lawns has been able to obtain an estimate of the relationship between sales and the amount spent on promotion in these two media: s = 2x12 - 10x22 - 2x1x2 + 18x1 + 34x2 s.t. x1 + x2 = 2 Solve.

x1 = 1.66; x2 = 0.33, Lagrange multiplier = 24

88) Sara has found an unlimited source of catnip so that is no longer a constraint. However, customer demand dictates that she produce 2.5 times more catnip balls than mice. Write the new constraint.

x1 = 2.5x2 OR x1 -2.5x2 = 0

Max Z = 5x1 + 6x2 Subject to: 17x1 + 8x2 ≤ 136 3x1 + 4x2 ≤ 36 x1, x2 ≥ 0 and integer What is the optimal solution? x1 = 2, x2 = 6, Z = 46 x1 = 3, x2 = 6, Z = 51 x1 = 6, x2 = 4, Z = 54 x1 = 4, x2 = 6, Z = 56

x1 = 4, x2 = 6, Z = 56

x1, x2, x3, x4, x5, x6 , x7, x8 ≥ 0 and integer

After months of broken promises, partial payments, and general stupidity, the landlord had no choice but to evict the long term tenants that had become little more than squatters in his first rental property. As he surveyed the damage and pondered a mix of repairs an upgrades, he scoured the latest statistics on what different upgrades might be worth in terms of increased rent. Beautifully refinished wood floors could increase the monthly rent about $100 and an upgrade to the kitchen would fetch $80 per month. The garage door needed replacement, but even though it would receive daily use, it was almost an order qualifier, and wouldn't net more than $20 per month. The house had always suffered from lack of a back door&8211;you had to access the backyard through the garage, so taking out a window and replacing it with a safety door would cost $250 and add only $15 to the monthly rent. The garage door would cost $350, the kitchen update would cost $1000 if he went with granite, and the floor refinish job would cost $400 to rent the buffer and buy the chemicals. It wouldn't be easy doing these upgrades; the garage door would take a half week, the back door one week, the floors two weeks and the tile three weeks. There was another way around these jobs though; instead of doing them himself, the landlord could always hire a professional in each field that could finish the job in half the time but would charge a pretty penny for that speed. Refinishing floors would cost $2700, upgrading the kitchen would cost $2500, replacing the back window with a door would cost $600, and installing a garage door opener would cost $350. Obviously if the model wants to upgrade the kitchen, it should be done by either the landlord or a subcontractor. As he creates the IP model, the landlord wants to leave the choice of whether to actually upgrade the kitchen up to the optimization algorithm. How should this constraint be written if he uses the following scheme for decision variables?

x3 + x4 ≤ 1

Obviously if the model wants to upgrade the kitchen, it should be done by either the landlord or a subcontractor. As he creates the IP model, the landlord wants to leave the choice of whether to actually upgrade the kitchen up to the optimization algorithm. How should this constraint be written if he uses the following scheme for decision variables? x3 - x4 = 1 x3 - x4 ≤ 1 x3 + x4 ≤ 1 x3 + x4 = 1

x3 + x4 ≤ 1

84) If the optimal solution includes x11 = 100 and x22 = 200, determine the remaining shipments that will result in a minimum cost of $1700.

x31 = 150, x42 = 50

After months of broken promises, partial payments, and general stupidity, the landlord had no choice but to evict the long term tenants that had become little more than squatters in his first rental property. As he surveyed the damage and pondered a mix of repairs an upgrades, he scoured the latest statistics on what different upgrades might be worth in terms of increased rent. Beautifully refinished wood floors could increase the monthly rent about $100 and an upgrade to the kitchen would fetch $80 per month. The garage door needed replacement, but even though it would receive daily use, it was almost an order qualifier, and wouldn't net more than $20 per month. The house had always suffered from lack of a back door&8211;you had to access the backyard through the garage, so taking out a window and replacing it with a safety door would cost $250 and add only $15 to the monthly rent. The garage door would cost $350, the kitchen update would cost $1000 if he went with granite, and the floor refinish job would cost $400 to rent the buffer and buy the chemicals. It wouldn't be easy doing these upgrades; the garage door would take a half week, the back door one week, the floors two weeks and the tile three weeks. There was another way around these jobs though; instead of doing them himself, the landlord could always hire a professional in each field that could finish the job in half the time but would charge a pretty penny for that speed. Refinishing floors would cost $2700, upgrading the kitchen would cost $2500, replacing the back window with a door would cost $600, and installing a garage door opener would cost $350. Suppose the landlord really wants the back door to be installed. For too long he has had to cut through the garage and he figures when he retires, this house will be a perfect downsize home for him to move into. How should the constraint for the back door be written if he uses the following scheme for decision variables?

x5 + x6 = 1

Due to increased sales, a company is considering building three new distribution centers (DCs) to serve four regional sales areas. The annual cost to operate DC 1 is $500 (in thousands of dollars). The cost to operate DC 2 is $600 (in thousands of dollars.). The cost to operate DC 3 is $525 (in thousands of dollars). Assume that the variable cost of operating at each location is the same, and therefore not a consideration in making the location decision. The table below shows the cost ($ per item) for shipping from each DC to each region. (BETTER CHART IN DOCUMENT) Region DC A B C D 1 1 3 3 2 2 2 4 1 3 3 3 2 2 3 The demand for region A is 70,000 units; for region B, 100,000 units; for region C, 50,000 units; and for region D, 80,000 units. Assume that the minimum capacity for the distribution center will be 500,000 units. 105) Define the decision variables for this situation.

y1 = 1 if DC1 is selected, 0 otherwise y2 = 1 if DC2 is selected, 0 otherwise y3 = 1 if DC3 is selected, 0 otherwise x1A = quantity shipped from DC 1 to Region A x1B = quantity shipped from DC 1 to Region B x1C = quantity shipped from DC 1 to Region C x1D = quantity shipped from DC 1 to Region D x2A = quantity shipped from DC 2 to Region A x2B = quantity shipped from DC 2 to Region B x2C = quantity shipped from DC 2 to Region C x2D = quantity shipped from DC 2 to Region D x3A = quantity shipped from DC 3 to Region A x3B = quantity shipped from DC 3 to Region B x3C = quantity shipped from DC 3 to Region C x3D = quantity shipped from DC 3 to Region D

24) In an unbalanced transportation problem, if supply exceeds demand, the shadow price for at least one of the supply constraints will be equal to ________.

zero

41) The first derivative of the fixed cost line is ________.

zero

42) The slope of a curve at its highest point equals: A) 0. B) 1. C) 2. D) 3.

81) How many constraints are required to model this as a linear program? A) 8 B) 9 C) 10 D) 12

In a transportation problem, items are allocated from sources to destinations:

at a minimum cost.

36) A one-way street in a downtown area should be modeled as a(n) ________ branch in a maximal flow model.

directed

19) The goal of the maximal flow problem is to maximize the amount of flow of items from an origin to a destination.

TRUE

2) Nodes represent junction points connecting branches.

TRUE

2) Nonlinear programming algorithms occasionally have difficulty distinguishing between local optima and the global optimum.

TRUE

21) In portfolio selection problems, risk is measured by the variance of the return on the portfolio.

TRUE

4) In a balanced transportation model where supply equals demand, all constraints are equalities.

TRUE

4) The slope of a curve at any point is equal to the derivative of the curve's function.

TRUE

4) The values assigned to branches typically represent distance, time, or cost.

TRUE

In a mixed integer model, all decision variables have integer solution values. True or False

FALSE

In a mixed integer model, the solution values of the decision variables are 0 or 1. True or False

FALSE

The ________ process is analogous to gambling devices.

Monte Carlo

Aunt Anastasia operates a small business: she produces seasonal ceramic objects to sell to tourists. For the spring, she is planning to make baskets, eggs, and rabbits. Based on your discussion with your aunt you construct the following table Your aunt also has committed to make 25 rabbits for a charitable organization. Based on the information in the table, you formulate the problem as a linear program. The Excel solution and the answer and sensitivity report are shown below. Aunt Anastasia feels that her prices are too low, particularly for her eggs. How much would her profit have to increase on the eggs before it is profitable for her to make and sell eggs?

$1.00

Given the following linear program that maximizes revenue: What is the maximum revenue at the optimal solution?

$160

Taco Loco is considering a new addition to their menu. They have test marketed a number of possibilities and narrowed them down to three new products, X, Y, and Z. Each of these products is made from a different combination of beef, beans, and cheese, and each product has a price point. Taco Loco feels they can sell an X for $17, a Y for $13, and a Z for $14. The company's management science consultant formulates the following linear programming model for company management. The sensitivity report from the computer model reads as follows: The optimal quantity of the three products and resulting revenue for Taco Loco is:

1.45 Z, 8.36 Y, and 0 Z for $129.09.

Figure 4 in document 124) Determine the maximal flow through the network in Figure 4. Assume that all branches are directed branches.

90) Consider the network diagram given in Figure 1. Assume that the numbers on the branches indicate the length of cable (in miles) between each pair of the six nodes on a telecommunication network. What is the minimum number of miles of cable to be used to connect all six nodes?

17 miles

126) What is the shortest route through the network in Figure 4?

18 via 1 to 3 to 6 to 7

Which of the following could not be a linear programming problem constraint?

1A + 2B ≠ 3

A crew of mechanics at the Department of Transportation garage make minor repairs to snowplows during the winter. The snowplows break down at an average rate of 4 vehicles per day and breakdowns are distributed according to the Poisson distribution. The mechanic can service an average of 7 vehicles per day with a repair time distribution that approximates a negative exponential distribution. Assume an 8 hour day. Determine the average time that a snowplow is out of service.

2.64 hours

93) Consider the curve 10x2 + 4x - 7. What is the second derivative at x = 8?

A bakery is considering hiring another clerk to better serve customers. To help with this decision, records were kept to determine how many customers arrived in 10-minute intervals. Based on 100 10-minute intervals, the following probability distribution and random number assignments developed. Suppose the next three random numbers were .18, .89 and .67. How many customers would have arrived during this 30-minute period?

The production manager for the Coory soft drink company is considering the production of two kinds of soft drinks: regular (R) and diet(D). Two of the limited resources are production time (8 hours = 480 minutes per day) and syrup (1 of the ingredients), limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case. What is the time constraint?

2R + 4D ≤ 480

125) Determine the minimum distance required to connect all nodes in Figure 4.

30 via 1 to 3, 1 to 4, 2 to 5, 3 to 2, 3 to 6, 5 to 7

Consider the following transportation problem: (BETTER CHART IN DOCUMENT) This one was a picture that didn't load 82) How many supply-side constraints are there? Write the supply-side constraints.

4 supply-side constraints x11 + x12 = 100 x21 + x22 = 200 x31 + x32 = 150 x41 + x42 = 50

What is the 95% confidence interval width for a sample with a mean of 50 and a standard deviation of 14 based on 75 observations?

46.83, 53.17)

51) Consider the network diagram given in Figure 2. Assume that the amount on each branch is the distance in miles between the respective nodes. What is the distance for the shortest route from the source node (node 1) to node 5? A) 13 B) 14 C) 15 D) 16

34) If price and demand are related by the function v = 15 + 15p and the fixed cost is $150 while the variable cost is $5, then the profit at a price of 20 Rupees is ________.

4575 Rupees

A baker uses organic flour from a local farmer in all of his baked goods. For each batch of bread (x1), he uses 4 pounds of flour. For a batch of cookies (x2), he uses 3 pounds, and for a batch of muffins (x3) he uses 2 pounds. The local farmer can supply him with no more than 24 pounds per week. The constraint that represents this condition is:

4x1 + 3x2 + 2x3 ≤ 24

90) A store has determined that the weekly sales of a product is related to the number of customers who visit the store and the square feet of shelf space, x, according to the following equation: -20x2 - 10C2 + 40Cx + 120x - 200C + 600. C represents the hundreds of customers who visit their store. If a store averages 200 customers per week, how many square feet of shelf space is required to maximize sales?

5 square feet

85) Use the network pictured and assume all labeled flows are forward flows. Suppose the reverse flows for each path are exactly half of the forward flows. What is the maximum flow through this network? A) 18 B) 28 C) 10 D) 8

The production manager for the Coory soft drink company is considering the production of two kinds of soft drinks: regular and diet. Two of her limited resources are production time (8 hours = 480 minutes per day) and syrup (1 of the ingredients), limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case. Which of the following is not a feasible production combination?

75R and 90D

49) The first step in the shortest route solution method is to: A) select the node with the shortest direct route from the origin. B) determine all nodes directly connected to the permanent set nodes. C) arbitrarily select any path in the network from origin to destination. D) make sure that all nodes have joined the permanent set.

68) What is the optimal production quantity?

90 units

Balanced transportation problems have which of the following type of constraints?

A balanced transportation model should have ________ constraints.

= or "equal to"

37) In a balanced transportation model where supply equals demand: A) all constraints are equalities. B) none of the constraints are equalities. C) all constraints are inequalities. D) none of the constraints are inequalities.

53) It was a bumper crop for hominy this year, and The Hominy Man hoped to set a price for a case that maximized profit. The annual fixed cost for the hominy harvesting and other equipment is $10,000 and the variable cost per case is $0.50. The price is related to demand according to the following equation: v = 800 - 16p. What is optimal profit? A) -$199 B) $199 C) $808 D) $10,400

55) The first step of the minimal spanning tree solution method is to: A) select any starting node. B) select the node closest to the starting node to join the spanning tree. C) select the closest node not presently in the spanning tree. D) arbitrarily select any path in the network from origin to destination.

66) Using the nodes of interest for the llamas, Fruit, Barn, Oak, Shade, Hay and Pond, what is the maximal flow from the Fruit to Hay? A) 11 B) 12 C) 13 D) 14

Zevon Enterprises Zevon Enterprises provides services for clients worldwide and to protect all parties to this course as well as Zevon, we shall refer to those services as X1, X2, and X3. Each of these services has its own special mix of needs for the resources the company has at its disposal. The X1 product requires three lawyers, seven guns, and $6,000; the X2 product requires two lawyers, five guns, and $4,000; and the X3 product requires four lawyers, six guns, and $7,000. Zevon has access to 5,000 lawyers, 10,000 guns, and $15,000,000. For ease of conversation, Zevon employees usually speak about dollars as "per thousand" so one of them asking for $7 means that they really need $7,000. Zevon's demand is variable depending on what they charge for it. For example, the X1 product's demand is 200 - 2.25p1. The demand for X2 is 300 - 3p2, and the demand for X3 is 400 - 3.5p3. The per unit profit for X1 through X3 can be calculated by subtracting the per unit cost from the sales price, so for X1, the profit is p1 - 2.25, for X2 the profit is p2 - 3, and for X3 the profit is p3 - 3.5. 54) What is an appropriate objective function for this scenario? A) Max Z = (p1 - 2.25)X1 + (p2 - 3)X2 + (p3 - 3.5)X3 B) Max Z = (p1 - 2.25p1) + (p2 - 3)(300 - 3.00p2) + (p3 - 3.5)(400 - 3.50p3) C) Max Z = 200X1 + 300X2 + 400X3 D) Max Z = 2.25(p1 - X1) + 3(p2 -X2) + 3.5(p3 - X3)

(picture/figure in document) 97) The camp nurse is stationed at Facility B. What is the shortest route from B to C?

B to G to E to C for a total of 30.

Which of the constraints best describes the relationship between the iPads for everyone and the speaker series? A - C = 0 A + C = 2 A + C = 1 A - C ≤ 1

A + C = 1

83) How much longer is the total arc length in the current network than twice the total arc length of the minimal spanning tree? A) 5 B) 10 C) 15 D) 20

If the solution values of a linear program are rounded in order to obtain an integer solution, the solution is: A) always optimal and feasible. B) sometimes optimal and feasible. C) always feasible. D) never optimal and feasible

Types of integer programming models are: total. 0-1. mixed. all of the above

All of the above

The following table represents the cost to ship from Distribution Center 1, 2, or 3 to Customer A, B, or C. 58) The constraint that represents the quantity supplied by DC 1 is: A) 4X1A + 6X1B + 8X1C ≤ 500. B) 4X1A + 6X1B + 8X1C = 500. C) X1A + X1B + X1C ≤ 500. D) X1A + X1B + X1C = 500.

A data envelopment analysis with an objective function value of 0.8 means the company is more efficient than its competitors since it expends only 80% of the effort to achieve the same results. True or False

FALSE

Data envelopment analysis indicates which type of service unit makes the highest profit. True or False

FALSE

Diet problems usually maximize nutritional value. True or False

FALSE

If we are solving a 0-1 integer programming problem, the constraint x1 + x2 = 1 is a mutually exclusive constraint. True or False

FALSE

If we are solving a 0-1 integer programming problem, the constraint x1 = x2 is a conditional constraint. True or False

FALSE

If we are solving a 0-1 integer programming problem, the constraint x1 ≤ x2 is a mutually exclusive constraint. True or False

FALSE

In a transportation problem, a demand constraint (the amount of product demanded at a given destination) is a less-than-or equal-to constraint (≤). True or False

FALSE

In most media selection decisions, the objective of the decision maker is to minimize cost. True or False

FALSE

Yowzah receives bids from four companies we'll call A, B, C, and D to supply product for the coming year. Renee DeCartes, the Yowzah VP of Plotting takes the bids and creates this graph to bring to the next executive meeting. The company with the lowest variable cost is:

41) In a network flow model, a directed branch: A) is a branch with a positive distance value. B) is a branch in which flow is possible in only one direction. C) is a branch on which the flow capacity is exhausted. D) is a branch in which flow is not possible in either direction.

69) The constraint for the quantity shipped from Atlanta is: A) X23 + X 24 = 1000. B) X23 + X 24 ≤ 1000. C) X23 + X 24 ≥ 1000. D) X13 + X 14 - X34 = 1000.

70) Using all the nodes of interest for the entire menagerie, what is the maximal flow from Grass to Pond? A) 20 B) 21 C) 22 D) 23

71) The objective of the maximal flow solution approach is to: A) maximize resource allocation. B) maximize the total amount of flow from an origin to a destination. C) determine the longest distance between an originating point and one or more destination points. D) determine the shortest distance between an originating point and one or more destination points.

72) What is the optimal solution to the Mantastic problem? A) $30,028 B) $30,820 C) $32,280 D) $32,820

77) Consider the network diagram given in Figure 3 with the indicated flow capacities along each branch. Determine the maximal flow on the following path: node 1 to node 2 to node 7 to destination node 9. A) 3 B) 4 C) 5 D) 6

42) In a network modeling problem, the linear programming decision variables are given by: A) source node. B) sink node. C) network branches. D) network nodes.

46) If we wanted to represent an urban transportation system as a network flow problem, which of the following would be represented as nodes? A) streets B) railway lines C) street intersections D) pedestrian right of ways

A systematic approach to model formulation is to first: A) construct the objective function. B) develop each constraint separately. C) define decision variables. D) determine the right hand side of each constraint.

When systematically formulating a linear program, the first step is to: A) construct the objective function. B) formulate the constraints. C) identify the decision variables. D) identify the parameter values.

If we are solving a 0-1 integer programming problem, the constraint x1 = x2 is a ________ constraint. multiple-choice mutually exclusive conditional corequisite

Corequisite

is a measure of the strength of the relationship between independent variable(s) and a dependent variable.

Correlation

Let xij = gallons of component i used in gasoline j. Assume that we have two components and two types of gasoline. There are 8000 gallons of component 1 available, and the demand gasoline types 1 and 2 are 11,000 and 14,000 gallons, respectively. Write the constraint stating that the component 1 cannot account for more than 35% of the gasoline type 1. A) x11 + x12 (.35)(x11 + x21) B) x11 + .35(x11 + x12) C) -.65x11 + .35x21 ≤ 0 D) .65x11 - .35x21 ≤ 0

Let xij = gallons of component i used in gasoline j. Assume that we have two components and two types of gasoline. There are 8000 gallons of component 1 available, and the demand gasoline types 1 and 2 are 11,000 and 14,000 gallons, respectively. Write the demand constraint for gasoline type 1. A) x21 + x22 = 11000 B) x12 + x22 = 11000 C) x11 + x21 ≤ 11000 D) x11+ x21= 11000

Refer to the figure below to answer the following questions. Figure 3 75) Consider the network diagram given in Figure 3 with the indicated flow capacities along each branch. Determine the maximal flow from source node 1 to destination node 9. A) 10 B) 11 C) 12 D) 13

99) A clean-up crew is stationed at facility D and wants to take the shortest route to each site. They usually clean up facilities C, E, A and F on the same day and therefore want the shortest route from D to each facility. Recommend a route for the crew to leave from D, clean up each facility one after the other, and return to facility D. (Assume all paths are accessible.) (picture/figure in document)

D to E to F to C to A to D. Total distance = 55. This is really a small version of the traveling salesman problem. Doing the minimal spanning tree prior to this problem may be helpful.

In a classic blending problem, revenue is maximized by subtracting cost from profit. True or False

FALSE

The ________ is a procedure for developing a consensus forecast about what will occur in the future.

Delphi method

Which constraint is most appropriate if the students can choose only three of these activities?

E + S +L + B ≤ 3

92) Determine the shortest route for delivery truck loaded with ignorance from a plant in Edmond to retail outlets in Ardmore and Lawton. State the total completion time in hours for each route.

Edmond-Woodward-Ardmore: 10 + 9 = 19 hours Edmond-Norman-Lawton: 6 + 10 = 16

107) During the harvest, the horse and llamas are herded up to the orchard where they are loaded down with fresh-picked fruit. Some of the fruit is taken to the pond to feed the catfish and the remainder is crated up underneath the shade trees. What is the shortest route to those locations; provide distance and the path?

From the fruit trees, the shortest route to the pond is 185' from Fruit to Oak to Pond. The shortest route to the Shade is 130' from Fruit to Barn to Shade.

106) The horse and llamas decide to join forces to develop a series of paths among their points of interest. All of them are spenders rather than savers, so they prefer to develop those paths using a minimum quantity of materials and labor. Which of the point to point paths should be used and what is the total distance?

Fruit-Barn = 20' Barn-Grass = 70' Barn-Oak = 80' Oak-Hay = 60' Hay-Shade = 50' Hay-Pond = 60' Total path distance is 340'

The production manager for the Coory soft drink company is considering the production of two kinds of soft drinks: regular (R) and diet (D). Two of her limited resources are production time (8 hours = 480 minutes per day) and syrup (1 of the ingredients), limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case. What is the objective function?

MAX $3R + $2D

25) The ________ reflects the approximate change in the objective function resulting from a unit change in the quantity (right-hand-side) value of the constraint.

Lagrange multiplier

26) The dual value of a resource in a nonlinear programming model is given by the ________.

Lagrange multiplier

moving averages react more slowly to recent demand changes than do ________ moving averages

Longer-period, shorter-period

is absolute error as a percentage of demand.

MAPD

Mantastic Devices designs and manufactures high-end support garments for men. The facilities in Manhattan and Atlanta serve as design and component manufacturing facilities. Components are then shipped to warehouses in Philadelphia or Knoxville, where they are held until final assembly is completed at either Memphis, New Orleans, or El Paso. Manufacturing capacity in Manhattan and Atlanta is 900 units. Demand at Memphis, New Orleans, and El Paso is 450, 500, and 610, respectively. The network representing the shipping routes is shown below. (picture you need to look at in the document) The costs for shipping between each facility is shown below. A blank cell indicates that shipping between two facilities is not permitted. (BETTER CHART IN DOCUMENT) Philadelphia Knoxville Memphis New Orleans El Paso Manhattan $4 $25 Atlanta $22 $3 Philadelphia $3 $20 $30 $40 Knoxville $3 $6 $15 $20 95) What is the objective function for the Mantastic problem? Use the notation Xij, where i and j correspond to the node numbers indicated in the diagram.

MIN 4X13 + 25X14 + 22X23 + 3X24 + 3X34 + 3X43 + 20X35 + 30X36 + 40X37 +

106) Write the objective function for this problem.

Min Z = 1x1A + 3x1B + 3x1C + 2x1D + 2x2A + 4x2B + 1x2C + 3x2D + 3x3A + 2x3B + 2x3C + 3x3D + 500y1 + 600y2 + 525y3

96) Walking trails will be constructed to connect all the facilities. In order to preserve the natural beauty of the camp (and to minimize the construction time and cost), the directors want to determine which paths should be constructed. Use this network to determine which paths should be built.

Minimal spanning tree shown in bold.

Consider the following network, which shows the location of various facilities within a youth camp and the distances (in tens of yards) between each facility. There is a swampy area between facilities A and E. (picture/figure in document) 98) Walking trails will be constructed to connect all the facilities. In order to preserve the natural beauty of the camp (and to minimize the construction time and cost), the directors want to determine which paths should be constructed. Use this network to determine which paths should be built.

Minimal spanning tree shown in bold. Total distance is 58.

Aunt Anastasia operates a small business: she produces seasonal ceramic objects to sell to tourists. For the spring, she is planning to make baskets, eggs, and rabbits. Based on your discussion with your aunt you construct the following table: Your aunt also has committed to make 25 rabbits for a charitable organization. Based on the information in the table, you formulate the problem as a linear program. MAX 2.5B + 1.5E + 2R s.t. The Excel solution and the answer and sensitivity report are shown below. The Answer Report: The Sensitivity Report: Aunt Anastasia's available hours for paint and seal have fallen from 80 hours to 60 hours because of other commitments. How will this affect her profits?

Profits will not change

1) A network is an arrangement of paths connected at various points through which items move.

TRUE

1) In a transportation problem, items are allocated from sources to destinations at a minimum cost.

TRUE

99) What is the optimal solution for the Mantastic problem?

The lowest total cost is $30,820. X13 =710, X24 = 900, X34 = 710, X45 = 450, X46 = 550, X47 = 610

101) How many constraints does this model have? Provide a description in English for each one, without writing it mathematically.

The model has r + c or 10 constraints, not counting the nonnegativity constraint. The row constraints could be summarized as "Each model must wear one outfit," and the column constraints can be summarized as "Each outfit must be worn by a model." Individually, the constraints would be articulated as: Zoe must wear one outfit. Yvette must wear one outfit. Xena must wear one outfit. Whisper must wear one outfit. Vajay must wear one outfit. The gown must be worn. The sport outfit must be worn. The couture must be worn. The avant-garde must be worn. The prêt-à-porter outfit must be worn.

Comedy Pasture A horse and two llamas are discussing the key areas of their domain on a lazy summer afternoon. The llamas favor the pond and shade and like to browse the fruit trees and oaks on the property, making their way to the barn only when their owner favors them with some oats. The horse prefers to graze the grass and hay for food and drink from the pond but will race up to the barn when the owner is handing out oats up there. Between the three of them, they have stepped off the distances between many of these key points several times and believe that they have developed an accurate map, shown below. As incredible as it may seem, neither the horse nor the llamas have had any training in management science, which is where you come in. (picture/figure in document) 101) The llamas are interested in developing a series of llama-only paths among their points of interest. As they have a limited budget, they'd prefer to develop those paths using a minimum quantity of materials and labor. Which of the point to point paths should be used and what is the total path distance?

The paths are: Fruit-Barn = 20' Barn-Oak = 80' Oak-Hay = 60' Hay-Shade = 50' Hay-Pond = 60' The total path distance is 270'

104) The horse is interested in developing a series of horse-only paths (named The Caballo Real) among its points of interest. The horse has a small budget and no one to help her, so it would prefer to develop those paths using a minimum quantity of materials and labor. Which of the point to point paths should be used and what is the total distance?

The paths needed are: Pond-Hay = 60' Hay-Oak = 60' Oak-Barn = 80' Barn-Grass = 70' Total path distance is 270'

The landlord ran the model in Excel and received the answer report contained in the table. Which of the following statements is correct? The rent will be $180 higher and the project will take 3.5 weeks to finish at a cost of $2900. The rent will be $195 higher and the project will take 3.5 weeks to finish at a cost of $3700. The rent will be $180 higher and the project will take 2.5 weeks to finish at a cost of $3700. The rent will be $195 higher and the project will take 2.5 weeks to finish at a cost of $2900.

The rent will be $180 higher and the project will take 3.5 weeks to finish at a cost of $2900.

103) Llamas are pack animals and the owner occasionally has them tote supplies from the barn to the fruit trees, oak trees, hay stand, shade area and down to the pond. What is the shortest route from the barn to these five other locations?

The shortest distance from the Barn to each destination is shown in the table: (better chart in the document) From Barn to Distance Route Fruit 20' direct Oak 80' direct Shade 110' direct Hay 140' Oak-Hay Pond 170' Oak-Pond

122) The origin node for this network is node number 1 and flow proceeds from node 1 to node 6. If each of the three longest branches is reduced in length by 10, what is the change in the shortest route through the network?

The shortest route changes from 1 - 3 - 6 = 21 to 1 - 2 - 5 - 6 = 18 for a total decrease of 3.

121) The origin node for this network is node number 1 and flow proceeds from node 1 to node 6. If the distance from node three to node six doubles, what is the change in the shortest route through the network?

The shortest route changes from 1 - 3 - 6 = 21 to 1 - 4 - 5 - 6 = 29, so a total increase of 8.

98) What is the total number of constraints for the Mantastic problem? How many decisions variables does it have?

There are seven constraints and twelve decision variables.

89) Sara has found an unlimited source of catnip so that is no longer a constraint. However, customer demand dictates that she produce 2.5 times more catnip balls than mice. How will this impact the prices that she should charge to maximize profit?

There is no impact. Prices remain the same. Note: The optimal quantities are 750 balls and 300 mice for a profit of $4050.

111) The department chair is eager to motivate the senior faculty to consider retirement and wants to burden them as much as possible. What should the model look like that otherwise meets departmental objectives?

Using the scheme Professor:Subject for decision variables, e.g. SI is Saba teaches Intro to Ops, Max Z = 3SI + 10SP + 12SQ + 16SC + 12SL + 7SM + 4GI + 19GP + 2GQ + 10GC + 8GL + 18GM + 5TI + 11TP + 4TQ + 14TC + 14TL + 3TM + 4DI + 11DP + 4DQ + 15DC + 17DL + 15DM SI + SP + SQ + SC + SL + SM = 3 GI + GP + GQ + GC + GL + GM = 3 TI + TP + TQ + TC + TL + TM = 3 DI + DP + DQ + DC + DL + DM = 3 SI + GI + TI + DI ≥ 6 SP + GP + TP + DP = 1 SQ + GQ + TQ+ DQ = 1 SC + GC + TC + DC = 1 SL + GL + TL+ DL = 1 SM + GM + TM + DM = 1 The difference between this model and the benevolent chair model is that this is formulated to maximize prep time and assigns each professor a three-course load. The benevolent chair model minimizes prep time and allows for a two-course teaching load.

If we are solving a 0-1 integer programming problem, the constraint x1 ≤ x2 is a ________ constraint.

conditional

The patriarch of the least funny comic strip in the history of the world must assign loathsome tasks to his children and spouse. Time estimates, based on historical performance, are provided in the table. (BETTER CHART IN DOCUMENT) Rake Cook Muck Pluck Slaughter Billy 12 10 10 16 13 Dolly 9 10 14 13 10 Jeffy 17 14 12 18 12 PJ 15 7 11 11 18 Thel 13 18 22 11 27 85) Using the data in the table: a) How many supply-side constraints are needed? b) How many demand-side constraints are needed? c) How many decision variables are involved in this assignment method?

a) 5, b) 5, c) 25

If we are solving a 0-1 integer programming problem, the constraint x1 ≤ x2 is a(n) ________ constraint.

conditional

33) The shortest route problem formulation requires a statement that mandates that what goes in to a node must equal what comes out of that node. This is referred to as ________.

conservation of flow

23) If a nonlinear programming model consists of a single nonlinear objective function and a single linear constraint, it is called a(n) ________ optimization problem.

constrained or nonlinear

"It's me or the cat!" the exasperated husband bellowed to his well-educated wife. "Hmmmm," she thought, "I could model this decision with a(n) ________ constraint."

contingency or mutually exclusive

Which of the following is not an integer linear programming problem?

continuous

An intern sets up a linear program to optimize the use of paper products in the men's washroom. The system of equations he develops is: His mentor studies the model, frowns, and admonishes the intern for violating which of the following properties of linear programming models?

additivity

In a balanced transportation model where supply equals demand:

all constraints are equalities.

23) In a(n) ________ transportation model where supply equals demand, all constraints are equalities.

balanced

34) In order to prevent the accumulation of inventory at transshipment points, they should be modeled as being ________ nodes.

balanced

In a multiperiod scheduling problem, the production constraint usually takes the form of:

beginning inventory - demand + production = ending inventory

The ________ method is based on the principle that the total set of feasible solutions can be partitioned into smaller subsets of solutions.

branch and bound

In an integer program, if building one facility required the construction of another type of facility, this would be written as: ________.

x1 = x2

Suppose the landlord really wants the back door to be installed. For too long he has had to cut through the garage and he figures when he retires, this house will be a perfect downsize home for him to move into. How should the constraint for the back door be written if he uses the following scheme for decision variables? x5 + x6 ≤ 1 x5 - x6 ≤ 1 x5 - x6 = 1 x5 + x6 = 1

x5 + x6 = 1

Which of these formulations of the budget constraint is correct? Assume that there are 20 students in this semesters MBA class. A + B + C + D + E ≤ 20 $15,000A + $500B + $15,000C + $200D + $100E ≤ $56,250 $750A + $25B + $15,000C + $10D + $5E ≤ $56,250 20A + 20B + C + 20D + 20E ≤ $56,250

$15,000A + $500B + $15,000C + $200D + $100E ≤ $56,250

95) Draw the network associated with the following constraints for a shortest route problem. X12 + X13 = 1 X12 - X24 = 0 X13 - X34 = 0 X24 + X34 - X45 = 0 X45 = 1

(Picture in document)

Cars arrive at a single-bay car wash at an average of 6 per hour according to the Poisson distribution. The wash time averages 4 minutes with a standard deviation of 1 minute, but the wash time is not defined by any distribution. What is the average number of cars in line?

.142

Poultry Processing processes chickens for fast food restaurants. The chickens arrive from the farms on trucks, in cages, at a rate of 8 trucks per hour according to the Poisson distribution. The quality standards of Poultry Processing require that the chickens be processed within 30 minutes, which includes the time from when the trucks arrive until the chickens are finished processing. What is the minimum average processing rate (in truckloads per hour) that must be designed for the machine in order to ensure that the cages will be processed, on the average, in 30 minutes or less? Assume processing time is exponentially distributed

10 trucks per hour

Taco Loco is considering a new addition to their menu. They have test marketed a number of possibilities and narrowed them down to three new products, X, Y, and Z. Each of these products is made from a different combination of beef, beans, and cheese, and each product has a price point. Taco Loco feels they can sell an X for $17, a Y for $13, and a Z for $14. The company's management science consultant formulates the following linear programming model for company management. The sensitivity report from the computer model reads as follows: Taco Loco is unsure whether the amount of beef that their computer thinks is in inventory is correct. What is the range in values for beef inventory that would not affect the optimal product mix?

17.78 to 30 pounds

Given the following data on the number of pints of ice cream sold at a local ice cream store for a 6-period time frame: Use a 2-period moving average to forecast demand for period 7.

290

58) The model is entered in Excel and executes to reveal that p2 equals $51.50. Which of these conclusions is correct? A) The contribution to net profit from service X2 is $7,056.75. B) The per unit profit for service X2 is $51.50. C) There is excess demand for service X1. D) The demand for X2 is 194.

Always

43) Mondo ran the problem in Excel but used "≤ 1" constraints everywhere instead of "= 1" constraints. The objective function is formulated correctly and the general structure of the constraints is also correct, except for the inequality. What is a reasonable conclusion that can be drawn from this formulation of the model? A) None of the outfits will be worn. B) There would be no difference in the model results from one with = constraints. C) A model may be assigned two different outfits. D) An outfit may be assigned to two different models.

44) If a firm's profit is Z = 12x - 6x2 + 30, and their minimum production level of x is equal to 0.5, then the level of x that maximizes profit is: A) .5. B) 1. C) 1.5. D) 2.

44) If we wanted to represent water resources as a network flow problem, which of the following would be represented as nodes? A) canals B) pumping stations C) rivers D) pipelines

45) A custom molder produces 6-ounce juice glasses and 10-ounce cocktail glasses. The per unit contribution for the juice glasses (x1) is equal to 60 - 5x1, and the per unit contribution for the cocktail glasses (x2) is 80 - 4x2. An expression for the total contribution is: A) 20 - 4x2 - 5x1. B) 60x1 - 5x12 + 80x2 - 4x22. C) 80x1 - 5x12 + 60x2 - 4x22. D) 20 - (4x2)(5x1).

47) The derivative of a function ________ the slope of the curve defined by that function. A) is larger than B) equals C) is smaller than D) is similar to

48) In the linear programming formulation of the shortest route problem, the constraint for each node represents: A) capacity on each path. B) conservation of flow. C) capacity on each branch. D) minimum flow.

43) A store has determined that the weekly sales of a product is related to the number of customers who visit the store and the square feet of shelf space, x, according to the following equation: -20x2 - 10C2 + 40Cx + 120x - 200. C represents the hundreds of customers who visit their store. If a store averages 200 customers per week, how many square feet of shelf space is required to maximize sales? A) 3 B) 4 C) 5 D) 1 or 9

44) Mondo ran the problem in Excel but wondered what would happen if he allowed his favorite model Xena to wear two outfits. She would be the first to walk the runway, then would change and also be the last model in the show. The sensitivity analysis for the original problem scenario is shown below. (look at document for better chart) Cell Name Final Value Shadow Price Constraint R.H. Side Allowable Increase Allowable Decrease $J$20 Gown 1 8 1 0 1 $K$20 Sport 1 8 1 0 1 $L$20 Leisure 1 5 1 0 0 $M$20 Cocktail 1 8 1 0 1 $N$20 Pret_a_Porter 1 9 1 0 1 $P$13 Zoe_wears 1 1 1 1 0 $P$14 Yvette_wears 1 0 1 1 0 $P$15 Xena_wears 1 -1 1 1 0 $P$16 Whisper_wears 1 0 1 0 1E+30 $P$17 Vajay_wears 1 4 1 0 0 What would happen if Mondo ran the model again, but this time changed the existing constraints to ≤ constraints and included a constraint that required Xena to model two separate looks? A) Xena would wear the pret-a-porter and the gown. B) Xena would wear the pret-a-porter and the cocktail. C) The overall fabulosity score would drop by 1. D) Xena would keep the same outfit.

49) The Lagrange multiplier reflects the appropriate change in the objective function resulting from a unit change in the ________ of the constraint equation. A) coefficient B) objective function C) right-hand side D) shadow price

Figure 4 78) Determine the maximal flow through the network in Figure 4. Assume that all branches are directed branches. A) 10 B) 12 C) 14 D) 16

If we are solving a 0-1 integer programming problem, the constraint x1 ≤ x2 is a ________ constraint. A) multiple-choice B) mutually exclusive C) conditional D) corequisite

48) Both linear and nonlinear programming models are examples of: A) goal programming models. B) simplex tableaus. C) constrained likelihood models. D) constrained optimization models.

52) The linear programming model for a transportation problem has constraints for supply at each ________ and ________ at each destination. A) destination, source B) source, destination C) demand, source D) source, demand

53) Which of the following assumptions is not an assumption of the transportation model? A) Shipping costs per unit are constant. B) There is one transportation route between each source and destination. C) There is one transportation mode between each source and destination. D) Actual total supply and actual total demand must be equal.

T/F: A conditional constraint specifies the conditions under which variables are integers or real variables.

T/F: If we are solving a 0-1 integer programming problem, the constraint x1 + x2 = 1 is a mutually exclusive constraint.

If we are solving a 0-1 integer programming problem, the constraint x1 ≤ x2 is a mutually exclusive constraint.

False

T/F: In a mixed integer model, some solution values for decision variables are integer and others can be non-integer.

T/F: In a problem involving capital budgeting applications, the 0-1 variables designate the acceptance or rejection of the different projects.

T/F: Rounding non-integer solution values up to the nearest integer value can result in an infeasible solution to an integer programming problem.

T/F: The production planner for Airbus showed his boss the latest product mix suggestion from their slick new linear programming model: 12.5 model 320s and 17.4 model 340s. The boss looked over his glasses at the production planner and reminded him that they had several half airplanes from last year's production rusting in the parking lot. No one, it seems, is interested in half of an airplane. The production planner whipped out his red pen and crossed out the .5 and .4, turning the new plan into 12 model 320s and 17 model 340s. This production plan is definitely feasible.

90) A partial solution to this problem is shown below, where the number 1 indicates when a reviewer is assigned to an applicant. Assign two reviewers to Applicant B and 1 additional reviewer to Applicant C. (BETTER CHART IN DOCUMENT) Applicant Reviewer A B C 1 X 2 X 1 3 X 4 1 5 X 6 X 7 X 8 1 X 9 X Demand 2 2 2 Assigned 2

This is one possible solution. Another is to assign reviewer 9 to applicant C. Applicant Reviewer A B C 1 0 0 1 2 0 0 1 3 0 1 0 4 1 0 0 5 0 1 0 6 0 0 0 7 0 0 0 8 1 0 0 9 0 0 0 Demand 2 2 2 Assigned 2 2 2

If we are solving a 0-1 integer programming problem, the constraint x1 + x2 ≤ 1 is a mutually exclusive constraint.

True

In a mixed integer model, some solution values for decision variables are integer and others can be non-integer.

True

The three types of integer programming models are total, 0-1, and mixed.

True

The constraint for the North American supply region is:

X11 + X12 + X13 + X14 - 5Y11 - 10Y12 ≤ 0

The objective function is

answer with 3 then 4 + 3

29) A form of the transportation problem in which all supply and demand values equal 1 is the ________ problem.

assignment

26) In a network flow problem, ________ connect nodes and show flow from one point to another.

branches

27) In a network flow problem, the values assigned to ________ typically represent distance, time, or cost.

branches

The indicator that results in total revenues being equal to total cost is called the:

break-even point.

In a 0-1 integer programming model, if the constraint x1 - x2 ≤ 0, it means when project 2 is selected, project 1 ________ be selected. can never must always is already can sometimes

can sometimes

A ________ is an up-and-down repetitive movement that repeats itself over a time span of more than 1 year

cyclical pattern

If fixed costs decrease, but variable cost and price remain the same, the break-even point:

decreases

In a(n) ________ problem, maximization of audience exposure may not result in maximization of total profit.

media selection

35) Determining where to build roads at the least cost within a park that reaches every popular sight represents a(n) ________ network model.

minimal spanning tree

The following is a graph of a linear programming problem. The feasible solution space is shaded, and the optimal solution is at the point labeled Z* This linear programming problem is a(n):

minimization problem

25) In a network flow problem, ________ represent junction points connecting branches.

nodes

A seed value is a(n):

number used to start a stream of random numbers

32) The cost to send a unit of product from supply source A to demand location B would be represented in the ________ of the linear programming statements.

objective function

The steps of the management science process are:

observation, problem definition, model construction, model solution, implementation.

Consider the following maximization problem. The optimal solution:

occurs where x = 0 and y = 2.

Simulations are normally done

on the computer.

36) In an assignment problem, all demand and supply values are equal to ________.

one

38) Once a decision maker has determined the shortest route to any node in the network, that node becomes a member of the ________.

permanent set

Cranky Jerry's Furniture Factory makes tables and chairs. If he is interested in a profit maximizing level of production, he should probably follow the example for the ________ problem found in this chapter.

product mix

An important factor to consider in analyzing a queuing system is the

queue discipline

Developing the cumulative probability distribution helps to determine

random number ranges

The arrival rate is the:

rate of arrivals to the service facility.

Investment problems maximize ________.

return on investments

For a maximization problem, assume that a constraint is binding. If the original amount of a resource is 4 lbs. and the range of feasibility (sensitivity range) for this constraint is from 3 lbs. to 6 lbs., increasing the amount of this resource by 1 lb. will result in the:

same product mix, different total profit.

In the Monte Carlo process, values for a random variable are generated by ________ a probability distribution

sampling from

34) A company plans to use an automatic guided vehicle for delivering mail to ten departments. The vehicle will begin from its docking area, visit each department, and return to the docking area. Cost is proportional to distance traveled. The type of network model that best represent this situation is ________.

shortest route

39) Determining where to build one way roads at the least cost within a park that takes visitors to every popular sight and returns them to the entrance represents a(n) ________ network model.

shortest route

If the solution values of a linear program are rounded in order to obtain an integer solution, the solution is

sometimes optimal and feasible

If the solution values of a linear program are rounded in order to obtain an integer solution, the solution is: never optimal and feasible. always feasible. always optimal and feasible. sometimes optimal and feasible.

sometimes optimal and feasible.

If a maximization linear programming problem consists of all less-than-or-equal-to constraints with all positive coefficients and the objective function consists of all positive objective function coefficients, then rounding down the linear programming optimal solution values of the decision variables will ________ result in a(n) ________ solution to the integer linear programming problem.

sometimes, optimal

If a maximization linear programming problem consists of all less-than-or-equal-to constraints with all positive coefficients and the objective function consists of all positive objective function coefficients, then rounding down the linear programming optimal solution values of the decision variables will ________ result in a(n) ________ solution to the integer linear programming problem. always, non-optimal never, non-optimal always, optimal sometimes, optimal

sometimes, optimal

The linear programming model for a transportation problem has constraints for supply at each ________ and ________ at each destination.

source, demand

The ________ for the computer solution of a linear programming problem requires all variables on the left side, and all numerical values on the right side of the inequality or equality sign.

standard form

40) The distance formula of d = will find the ________ distance between two locations.

straight line

A shadow price reflects which of the following in a maximization problem?

the marginal gain in the objective that would be realized by adding one unit of a resource

32) A courier service located at the south edge of downtown dispatches three bicycle couriers with identical sets of architectural renderings that must go to three different downtown law offices as quickly as possible. This problem is a likely candidate for analysis using ________.

the shortest route solution/algorithm

Compared to blending and product mix problems, transportation problems are unique because:

the solution values are always integers

39) The objective of a facility location problem is to minimize ________.

the total distance traveled

91) Consider the curve 10x2 + 4x - 7. What is the lowest point on this curve?

x = -0.2

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