BIT 2406 FINAL
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
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.
.65x11 -.35x21 ≤ 0
What is the slope of the regression equation developed when the Sales data are used to predict the Pounds (use sales only, not time)?
0.92
In adjusted exponential smoothing, the closer beta is to ________, the stronger a trend is reflected.
1
Use this diagram for the next two questions. Determine the maximal flow through the network in Figure 4. Assume that all branches are directed branches.
13
Given forecast errors of 6, 4, 0 and -2, what is the mean squared error?
14
A newly opened bed-and-breakfast projects the following: Monthly fixed costs $8000 Variable cost per occupied room per night $40 Revenue per occupied room per night $165 The expression for total REVENUE per month is:
165x
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
The owner decides that the safest forecasting approach is exponential smoothing with an alpha of 0.8. He uses the January demand as the January forecast just to get the ball rolling. Help him out by finding the forecast for April.
497.4
If the calories required in the diet go up by 50, what will be the total cost of the optimal diet?
56 cents
The formula in cell C8 is
=SUM(C5:C7)
Which line is represented by the equation 2X + Y ≥ 8?
BF
Continuing from the diet problem of the previous two questions, examine the solver dialogue box: The formula for the model decision variables that should be entered into the "By Changing Variable Cells:" window in the Solver window above is
C5:C14
The demand requirements are going to be modified so that one more TV set will be required at either New York or Dallas or Detroit. Which one of these demand changes would have the greatest impact on the total cost?
Dallas
One of the formulas for the constraints that should be entered in the "Subject to the Constraints:" window in the Solver window is
F15 ≥ F17
Multiple optimal solutions occur only when constraints are parallel to each other.
False
The Excel formulas for the Fat and Cholesterol constraints can be reflected in the "Subject to the constraints:" window as G15:H15 >= F17:G17.
False
Use this picture for the next four questions. Which of the following points is not feasible?
G
A business owner is trying to decide whether to buy, rent, or lease office space and has constructed the following payoff table based on whether business is brisk or slow. Alternative Brisk Slow Buy 90 -10 Rent 70 40 Lease 60 55 The maximin strategy is:
Lease
A business owner is trying to decide whether to buy, rent, or lease office space and has constructed the following payoff table based on whether business is brisk or slow. Alternative Brisk Slow Buy 90 -10 Rent 70 40 Lease 60 55 The equal likelihood criterion strategy is:
Lease
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.
________ methods assume that what has occurred in the past will continue to occur in the future.
Time series
The equation for constraint DH is:
X + 2Y ≥ 8.
The constraint for the North American supply region is:
X11 + X12 + X13 + X14 - 5Y11 - 10Y12 ≤ 0.
The constraint for the South Asia demand region is:
X13 + X23 + X33 + X43 = 7.
The constraint for Philadelphia is:
X13 + X23+ X43- X34 - X35 - X36 - X37 = 0
Regret is the difference between the payoff from the:
best decision and all other decision payoffs.
Coefficient of determination is the percentage of the variation in the ________ variable that results from the ________ variable.
dependent, independent
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
The ________ is the expected value of the regret for each decision.
expected opportunity loss
Which additional resources would you recommend that Aunt Anastasia try to obtain?
kiln
In an assignment problem:
one task can be done by only one agent.
The term ________ refers to testing how a problem solution reacts to changes in one or more of the model parameters.
sensitivity analysis
A shadow price reflects which of the following in a maximization problem with resource constraints?
the marginal gain in the objective that would be realized by adding one unit of a resource
At the break-even point:
total revenue equals total cost.
Suppose the landlord really wants the back door to be installed. How should the constraint for the back door be written if he uses the following scheme for decision variables? x1 = contractor works on wood floors x2 = landlord works on wood floors x3 = contractor works on kitchen tile x4 = landlord works on kitchen tile x5 = contractor works on back door x6 = landlord works on back door x7 = contractor works on garage door x8 = landlord works on garage door
x5+ x6= 1
If the number of TVs required in New York goes up by 10, what will be the total cost of the optimal shipping plan?
$7460
Which of the following possible values of alpha would cause exponential smoothing to respond the most slowly to sudden changes in forecast errors?
0.01
The following data represents quarterly sales of lawnmowers. What is the seasonal index for the third quarter? (Round to the nearest hundredth.)
0.30
In exponential smoothing, the closer alpha is to ________, the greater the reaction to the most recent demand.
1
For the city you identified in the previous question, the most additional amount of this demand we could require before the marginal cost changes is
100 TV sets
A business owner is trying to decide whether to buy, rent, or lease office space and has constructed the following payoff table based on whether business is brisk or slow. Alternative Brisk Slow Buy 90 -10 Rent 70 40 Lease 60 55 If the probability of brisk business is .40 and for slow business is .60, the expected value of perfect information is:
12
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
The formula in cell C11 for cost has several terms in it. One of them is:
16*C5
The manager of "Skis 4 U" is preparing a forecast for February of 2020. Demand exhibits both trend and seasonality. The trend equation for annual demand is y = 14,000 + 200t, where t = 1 for 2011. The seasonal index for February is 0.20. The forecast for February 2020 is:
16,000*0.20
For the nutrient you identified in the previous question, the most additional amount of this nutrient we could require before the marginal cost changes is
2.5 units
It costs $50,000 to start a production process. Variable cost is $25 per unit and revenue is $45 per unit. What is the break-even point?
2500 units
Determine the minimum distance required to connect all nodes in Figure 4 (above). Assume all arcs go both ways.
26
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
Given forecast errors of 6, 4, 0 and -2, what is the mean absolute deviation?
3
The owner decides that the safest forecasting approach is a weighted moving average using 0.6, 0.3, and 0.1 for the most recent three. Help him out by finding the forecast for June.
573.9
Taco sales by month are shown in the table. Use this for the next 3 questions. Month Sales January 474 February 485 March 501 April 588 May 579 June 673 July 594 August 679 September 608 October 699 November 732 December 732 The owner decides that the safest forecasting approach is a moving average of two periods. Help him out by finding the forecast for June.
583.5
Use this information for the next two questions. 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. Using 1 to represent January, 2 to represent February, and so on, what is the intercept for the regression equation that predicts the pounds of supplies available as a function of time?
59.55
The constraints of the problem are: 3x + 2y ≥ 24 3x + 5y ≥ 30 x ≤ 12 y ≤ 12 x ≥ 0, y ≥ 0 What is the x coordinate of point B (note: the picture is not exact)?
6 2/3
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?
60
Given an actual demand of 59, a previous forecast of 64, and an alpha of .3, what would the forecast for the next period be using simple exponential smoothing?
62.5
A newly opened bed-and-breakfast projects the following: Monthly fixed costs $8000 Variable cost per occupied room per night $40 Revenue per occupied room per night $165 Let x be the number of nights of room reservations in a given month. The expression for total COST per month is:
8000 + 40x
A newly opened bed-and-breakfast projects the following: Monthly fixed costs $8000 Variable cost per occupied room per night $40 Revenue per occupied room per night $165 The expression for the BREAKEVEN volume per month is:
8000/(165-40)
Use this information for the next 8 questions. The diet problem in chapter 4 of your text involved minimizing the cost of a combination of up to 10 foods. The decision variables xi represented the number of servings of the ith food included in the diet. Seven nutrition constraints were included, as indicated in the formulation and excel worksheet below. The problem was solved using solver, and the solver dialog box and sensitivity report follow. The formula in cell C19 for cost is:
=SUMPRODUCT(C5:C14,E5:E14)
The formula in cell F15 is
=SUMPRODUCT(C5:C14,F5:F14)
If this is a minimization (with positive coefficients), which extreme point is the optimal solution? Note that the dashed line is steeper than the line connecting A and B.
A
A manufacturer must decide whether to build a small or a large plant at a new location. Demand at the location can be either low or high, with probabilities estimated to be 0.4 and 0.6, respectively. If a small plant is built, and demand is high, the production manager may choose to maintain the current size or to expand. The net present value of profits is $223,000 if the firm chooses not to expand. However, if the firm chooses to expand, there is a 50% chance that the net present value of the returns will be 330,000 and a 50% chance the estimated net present value of profits will be $210,000. If a small facility is built and demand is low, there is no reason to expand and the net present value of the profits is $200,000. However, if a large facility is built and the demand turns out to be low, the choice is to do nothing with a net present value of $40,000 or to stimulate demand through local advertising. The response to advertising can be either modest with a probability of .3 or favorable with a probability of .7. If the response to advertising is modest, the net present value of the profits is $20,000. However, if the response to advertising is favorable, then the net present value of the profits is $220,000. Finally, if the large plant is built and the demand happens to be high, the net present value of the profits $800,000. Determine the payoff for each decision and event node. Which alternative should the manufacturer choose?
Build a large plant, advertise if demand is low
A business owner is trying to decide whether to buy, rent, or lease office space and has constructed the following payoff table based on whether business is brisk or slow. (This information will be used for questions 5 through 8. Alternative Brisk Slow Buy 90 -10 Rent 70 40 Lease 60 55 The maximax strategy is:
Buy
The solver dialogue box for this problem is: The formula for the model decision variables that should be entered into the "By Changing Variable Cells:" window in the Solver window above is
C5:E7
One of the formulas for the constraints that should be entered in the "Subject to the Constraints:" window in the Solver window is
C8=C10
The nutrient requirements are going to be modified so that one more unit of Iron or calcium or protein will be required. Which one of these nutrient changes would have the greatest impact on the total cost of the diet?
Calcium
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:
D
Which of the following constraints has a surplus greater than 0?
DH
The ________ is a procedure for developing a consensus forecast about what will occur in the future.
Delphi method e
Use the following picture for the next three questions. A graphical representation of a linear program is shown below. The shaded area represents the feasible region, and the dashed line in the middle shows the slope of the objective function. If this is a maximization (with positive coefficients), which extreme point is the optimal solution?
E
A shipping company manager wants to determine the best routes for the trucks to take to go from the main warehouse to each of their destinations. This problem can be solved using the minimal spanning tree.
False
Correlation measures the strength of relationship between the x and y variables and the closer it is to 1 or -1, the greater the proof that the level of x determines the level of y.
False
For a profit maximization problem, if the allowable increase for a coefficient in the objective function is infinite, then profits are unbounded.
False
If average forecast error is positive, it indicates that the forecast is biased high.
False
In a balanced transportation problem, a demand constraint (the amount of product demanded at a given destination) is a less-than-or equal-to constraint (≤).
False
In a mixed integer model, the solution values of the decision variables must be 0 or 1.
False
Proportionality means the slope of a constraint is proportional to the slope of the objective function.
False
The optimal solution for a graphical linear programming problem is always the corner point that is the farthest from the origin.
False
The sensitivity range for an objective function coefficient is the range of values over which the profit does not change.
False
The shortest route network problem could help identify the best plan for running cables for televisions throughout a building. Each television needs to be connected to the network.
False
Which of these routes for the horse is actually the shortest between the pair of nodes?
Grass - Pond = 190'
________ 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
Suppose the charitable organization contacted Aunt Anastasia and told her that they had underestimated the amount of rabbits they needed. Instead of 25 rabbits, they need 35. How would this affect Aunt Anastasia's profits?
Profits would decrease by $5.
Cost/benfit information is available. Wood floors could increase the monthly rent about $100 and an upgrade to the kitchen tile would fetch $80 per month. Garage door replacement wouldn't net more than $20 per month. A safety door would cost $250 and add only $15 to the monthly rent. The garage door would cost $350, the kitchen tile update would cost $1000, and the wood 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 tile 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 cost $2900.
If we change the constraint quantity to a value outside the sensitivity range for that constraint quantity, the shadow price will change.
True
Longer-period moving averages react more slowly to recent demand changes than do shorter-period moving averages.
True
The Excel formulas for the demand constraints can be reflected in the "Subject to the constraints:" window as C8:E8 = C10:E10.
True
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
The sensitivity range for a constraint quantity value is the range over which the shadow price is valid.
True
The terms in the objective function or constraints are additive.
True
Madlantic Devices designs and manufactures high-end medical devices. The facilities in Madison 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 Dayton, Bloomington, or Albany. Manufacturing capacity in Madison and Atlanta is 1000 units. Demand at Dayton, Bloomington, and Albany is 450, 500, and 610, respectively. The network representing the shipping routes is shown below.
X13+ X 14 ≤ 1000
Which of these constraints will ensure that a low capacity facility is notbuilt in South America?
Y21=0
Which of these constraints will ensure that either a low capacity or a high facility capacity facility is built in the European supply region?
Y41 + Y42 = 1
Which of the following is an equation or an inequality that expresses a resource restriction in a mathematical model?
a constraint
The assignment problem constraint x31 + x32 + x33 + x34 ≤ 2 means:
agent 3 can be assigned to no more than 2 tasks.
The first step of the maximal flow solution method is to:
arbitrarily select any path in the network from origin to destination.
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
The Hurwicz criterion multiplies the:
best payoff by the coefficient of optimism.
The constraint AJ: a. contains the optimal solution. b. does not contain feasible points. c. None of the answers are true d. is a binding constraint.
c. none of the answers are true
The ________ is computed by multiplying each decision outcome under each state of nature by the probability of its occurrence.
expected value
Determining the worst payoff for each alternative and choosing the alternative with the best worst is called:
maximin.
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*. Assuming that the coefficients in the objective function are positive, this linear programming problem is a(n): Correct!
minimization problem
The minimal spanning tree problem determines the:
minimum total branch lengths connecting all nodes in the network
Let: rj = regular production quantity for period j, oj =overtime production quantity in period j, ij = inventory quantity at the end of period j, and dj = demand quantity in period j. Correct formulation of the demand constraint for a multiperiod scheduling problem is:
r2 + o2 + i1 - i2 = d2
For a linear programming problem, assume that a given resource has not been fully used. We can conclude that the shadow price associated with that constraint:
will have a value of zero.
For the constraints given below, which point is in the feasible region of this minimization problem? (1) 14x + 6y ≤ 42 (2) x + 3y ≥ 6
x = 1; y = 2
A landlord is considering upgrades and repairs, including wood floors, kitchen tile, a new back door, and a repaired garage door. The landlord could do these things himself or hire a contractor. The contractor could finish the job in half the time but would charge more. The landlord wants to leave the choice of whether to actually upgrade the kitchen tile up to the optimization algorithm. How should this constraint be written if he uses the following scheme for decision variables? x1 = contractor works on wood floors x2 = landlord works on wood floors x3 = contractor works on kitchen tile x4 = landlord works on kitchen tile x5 = contractor works on back door x6 = landlord works on back door x7 = contractor works on garage door x8 = landlord works on garage door
x3+ x4≤ 1