Agec 3413 test 2

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4) When using a linear programming model to solve the diet problem, the objective is generally to maximize nutritional content.

FALSE

5) Diet problems usually maximize nutritional value.

FALSE

91) Formulate the appropriate objective function for this scenario.

Max Z = 5,000x1 + 3,000x2 + 700x3 + 200x4 Where x1 = Newspaper advertisements x2 = Radio advertisements x3 = Tweets x4 = Facebook postings

92) Formulate the appropriate LP model for this scenario.

Max Z = 5,000x1 + 3,000x2 + 700x3 + 200x4 Where x1 = Newspaper advertisements x2 = Radio advertisements x3 = Tweets x4 = Facebook postings Subject to: $500x1 + $250x2 + $125x3 + $15x4 ≤ $3,500 x1 ≤ 4 x2 ≤ 24 x3 ≤ 3 x4 ≤ 4

28) 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

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

TRUE

13) 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

14) 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

17) Blending problems usually require algebraic manipulation in order to write the LP in "standard form."

TRUE

21) Data envelopment analysis problems are usually maximization problems.

TRUE

23) 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

9) In a balanced transportation model, supply equals demand such that all constraints can be treated as equalities.

TRUE

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

0-1

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

0-1 integer

84) For the production combination of 16 pumpkin, 125 chipotle-adobo, and 124 basement, which resource is not completely used up and how much is remaining?

1 ounce salt, 325 ounces herbs, and 768 ounces maize

The Exorbitant Course Fees The $75 per credit hour course fee tacked on to all the MBA classes has generated a windfall of $56,250 in its first semester. "Now we just need to make sure we spend it all," the Assistant Dean cackled. She charged the Graduate Curriculum Committee with generating a shopping list before their next meeting. Four months later, the chairman of the committee distributed the following. As the professor for the quantitative modeling course, he tended to think in terms of decision variables, so he added the left-most column for ease of use. Decision Variable Item Cost Note A iPads for everybody $750/unit Must get a cover if these are purchased B iPad covers with MBA logo $25/unit Not needed unless we buy iPads C Speaker series $15,000 Can't afford both this and the iPads D Subscriptions to the Wall Street Journal $10/unit Don't need if we have the electronic version E Subscriptions to the electronic version of the Wall Street Journal $5/unit Worthless without the iPads 106) What is a full set of constraints for this problem if there are 30 MBA students enrolled this semester?

22,500A + 750B + 15,000C + 300D + 150E ≤ 56,250 A + C ≤ 1 A - B = 0 E - A ≤ 0 D + E ≤ 1

96) What is the optimal answer to this problem?

320 units from 1 to A 80 units from 2 to A 340 units from 2 to C 400 units from 3 to B 120 units from 3 to C total cost of $7,120

106) What is a full set of constraints if the farmer wants this flock to produce less than 100 decibels of noise and more than 5 pounds of fertilizer, consume less than 10 pounds of layer pellets, and achieve a total plumage score of at least 75?

3L + 9C+ 6B > = 75 2L + 8C + 5B <= 100 3L + 2C + 4B >= 80 5L + 4C + 8B <= 160

98) Quickbrush Paint Company makes a profit of $2 per gallon on its oil-base paint and $3 per gallon on its water-base paint. Both paints contain two ingredients, A and B. 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. The company wishes to use linear programming to determine the appropriate mix of oil-base and water-base paint to produce to maximize its total profit. How much oil-based and water-based paint should the Quickbrush make?

9167 gallons of water-base paint and 5833 gallons of oil-base paint Andy Tyre manages Tyre's Wheels, Inc. Andy has received an order for 1000 standard wheels and 1200 deluxe wheels for next month, and for 750 standard wheels and 1000 deluxe wheels the following months. He must fill all the orders. The cost of regular time production for standard wheels is $25 and for deluxe wheels, $40. Overtime production costs 50% more. For each of the next two months there are 1000 hours of regular time production and 500 hours of overtime production available. A standard wheel requires .5 hour of production time and a deluxe wheel, .6 hour. The cost of carrying a wheel from one month to the next is $2.

36) A balanced transportation model should have ________ constraints.

= or "equal to"

43) What is the constraint for salt? A) 2P + 6C + 1.75B ≤ 1000 B) 2P + 3C + 4B ≤ 1000 C) 3P + 6C + 3.5B ≤ 2000 D) 3P + 3C + 4B ≤ 2000

44) The landlord ran the model in Excel and received the answer report contained in the table. Which of the following statements is correct? Variable Cells Cell Name Original Value Final Value $G$4 wood floors contractor 1 0 $H$4 wood floors self 1 1 $G$5 kitchen tile contractor 1 1 $H$5 kitchen tile self 1 0 $G$6 back door contractor 1 0 $H$6 back door self 1 0 $G$7 garage door opener contractor 1 0 $H$7 garage door opener self 1 0 (better graph of this in the document) A) The rent will be $180 higher and the project will take 3.5 weeks to finish at a cost of $2900. B) The rent will be $195 higher and the project will take 2.5 weeks to finish at a cost of $2900. C) The rent will be $180 higher and the project will take 2.5 weeks to finish at a cost of $3700. D) The rent will be $195 higher and the project will take 3.5 weeks to finish at a cost of $3700.

46) What is an appropriate objective function for this fast food vignette? A) Max Z = 2.75N + 4B + 2Q + 3E B) Min Z = 400C + 150M + 400B + 250T C) Min Z = 2.75N + 4B + 2Q + 3E D) Max Z = 400C + 150M + 400B + 250T

49) 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? A) 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 B) 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 C) Min Z = 100JS + 95JP + 120JH + 60JL + 110CS + 55CP + 70CH + 90CL + 130CTe + 90GS + 60GP + 110GH + 130GL + 95GTu JS + CS + GS ≤ 1 JP + CP + GP ≤ 1 JH + CH + GH ≤ 1 JL + CL + GL ≤ 1 D) Min Z = 100JS + 95JP + 120JH + 60JL + 110CS + 55CP + 70CH + 90CL + 130CTe + 90GS + 60GP + 110GH + 130GL + 95GTu JS + JP + JH + JL + CS + CP + CH + CL + CTe + GS + GP + GH + GL + GTu = 3

50) Which of these statements about the sensitivity report is best? Look at the chart A) There are no Burritacos being made. B) If the Nacholupa has a cost reduction of more than 0, none will be made. C) The company can make up to 1E + 30 Burritacos. D) The company can make an additional 0.25 Nacholupas if they want to with the leftover ingredients.

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

52) What is an appropriate objective function for this scenario? A) Max Z = 5,000N + 3,000R + 700T + 200F B) Max Z = 500N + 250R + 125T + 15F C) Min Z = 500N + 250R + 125T + 15F D) Min Z = 5,000N + 3,000R + 700T + 200F

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

56) What is the proper interpretation of the shadow price for Facebook?(look at the chart) A) Every additional dollar spent on Facebook advertising gains 20 customers as long as the number of postings does not exceed 233. B) Every additional dollar spent on Facebook advertising gains 20 customers as long as the number of postings does not exceed 229. C) If they spend $4, then can reach 20 customers. D) If they spend less than $20, they can reach 229.333 customers.

59) 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

61) 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? A) $380 B) $400 C) $420 D) $440

62) Which of the following is an appropriate objective function? A) Max Z = 5L + 2C + 4.5B B) Max Z = 10L + 10C + 10B C) Min Z = 5L + 2C + 4.5B D) Min Z = 10L + 10C + 10B

66) 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

72) The constraint for distribution center 1 is: A) X11 + X12 + X13 + X14 - 500y1 ≤ 0. B) X11 + X12 + X13 + X14D + 500y1 ≤ 0. C) X11 + X12 + X13 + X14 ≤ 500. D) X11 + X12 + X13 + X14 ≥ 500.

73) The objective function is (look at the document for the options because the equations didn't copy and paste well) A) Min Z = + B) Min Z = + C) Min Z = + D) Min Z = +

75) The constraint for the entrées is: A) AaE + AlE + JOE + EE + JuE + KE + LE + McE + MrE + TE ≥ 5. B) AaE + AlE + JOE + EE + JuE + KE + LE + McE + MrE + TE ≤ 5. C) AaE + AlE + JOE + EE + JuE + KE + LE + McE + MrE + TE > 5. D) AaE + AlE + JOE + EE + JuE + KE + LE + McE + MrE + TE < 5.

79) Which student experiences the greatest loss of contribution to the objective function value if this scenario was modeled as a 0-1 problem instead of an integer model? A) Lindy B) Marlene C) MacGregor D) There is no difference in any student's contribution.

Saba conducts regular tours of his favorite city in the world, Paris. Each semester he selects among the finest students in the university and escorts them to the City of Lights. In addition to a world-class education on conducting business in Europe, he arranges a number of cultural outings for them to help them immerse themselves in all that France has to offer. He collects an extra $100 from each student for this purpose and limits his tour group to ten lucky individuals. Some of the events (and their prices) he proposes to the students include: Eiffel Tower visit, $40 per student, E Paris Sewer spelunking, $20 per student, S Half day passes to the Louvre, $60 per student, L Bon Beret tour, $50 per student, B So much to do and so little time! 65) Which constraint is most appropriate if the students can choose only three of these activities? A) E + S + L + B ≤ 3 B) $40E + $20S + $60L + $50B ≤ $100 C) E + S + L + B ≥ 2 D) E + S + L + B ≤ 4

The Deadbeats 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 and 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 - 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. 40) 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? x1 = contractor works on wood floors x2 = landlord works on wood floors x3 = contractor works on kitchen tile x4 = contractor works on kitchen tile x5 = contractor works on back door x6 = contractor works on back door x7 = contractor works on garage door x8 = contractor works on garage door A) x3 + x4 ≤ 1 B) x3 + x4 = 1 C) x3 - x4 ≤ 1 D) x3 - x4 = 1

113) The assistant manager had taken a management science class a few years before and while she knew enough to formulate the problem and implement it in Excel, the only sensitivity training she had ever received had to do with being more empathetic to the plight of her minimum wage workforce. Help her interpret the sensitivity report for the cheese and meat constraints as it appears below. (look at the chart)

All 400 ounces of the cheese and 150 ounces of the meat are used in the optimal product mix. If the assistant manager could buy an ounce of cheese for 25 cents or less, they should do that up to an additional 16.6 ounces of cheese. If they were to waste cheese, each ounce lost would effectively lose them 25 cents up to losing 233 ounces. Additional meat should be purchased up to a price of 12.5 cents per ounce and up to an additional 110 ounces. Wasting an ounce of meat costs 12.5 cents per ounce up to a loss of 10 ounces.

41) 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? x1 = contractor works on wood floors x2 = landlord works on wood floors x3 = contractor works on kitchen tile x4 = contractor works on kitchen tile x5 = contractor works on back door x6 = contractor works on back door x7 = contractor works on garage door x8 = contractor works on garage door A) x5 + x6 ≤ 1 B) x5 + x6 = 1 C) x5 - x6 ≤ 1 D) x5 - x6 = 1

45) The landlord ran the model in Excel and received the sensitivity report for the constraints as contained in the table. Which of the following statements is correct? look at the graph in the chart! A) If there are 2 more weeks available for work, it would be possible to increase rent by $27.28 per week B) Given the scenario, it is evident that a constraint is missing. C) If the landlord installed two garage doors, rent could be increased by $23.64. D) Given the scenario, it is evident that the objective function is misstated.

47) 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? A) JS + JP + JH + JL + CS + CP + CH + CL + CTe + GS + GP + GH + GL + GTu ≤ 3 B) JS + JP + JH + JL = 1 CS + CP + CH + CL + CTe = 1 GS + GP + GH + GL + GTu = 1 C) JS + CS + GS ≤ 1 JP + CP + GP ≤ 1 JH + CH + GH ≤ 1 JL + CL + GL ≤ 1 D) JS + JP + JH + JL + CS + CP + CH + CL + CTe + GS + GP + GH + GL + GTu = 3

53) 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

56) 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.

60) 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

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

63) The poultry farmer would like to generate 80 ounces of fertilizer per week while feeding a maximum of 160 ounces of layer pellets each week. Which of these constraints is correct? A) 3L + 2C + 4C ≤ 80 B) 5L + 4C + 8B ≤ 160 C) 5L + 4C + 8B ≥ 160 D) 5L + 4C + 8B ≥ 80

73) 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.

74) 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.

76) Aaron's constraint is: A) AaE + AaS + AaD ≤ 2. B) AaE + AaS + AaD = 2. C) AaE + AaS + AaD ≥ 2 D) AaE + AaS + AaD < 3

77) The expected returns on investment of the three stocks are 6%, 8%, and 11%. An appropriate objective function is: A) MAX .06X1 +.08X2 +.11X3. B) MAX .06(15)X1 +.08(47.25)X2 +.11(110)X3. C) MAX 15X1 + 47.25X2 +.110X3. D) MAX (1/.06)X1 +.(1/08)X2 + (1/.11)X3.

80) What is the optimal answer to this problem? A) $7202 B) $7120 C) $7220 D) $7320

81) 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. A) exactly 1, 2 B) exactly 2, 4 C) at least 2, 4 D) at most 1, 2

83) 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

84) 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

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

Blending

39) 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.

40) 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.

42) For the production combination of 100 bags of each flavor of chips, which of the three resources is (are) not completely used? A) maize only B) salt and maize only C) herbs maize and salt D) salt and herbs only

43) The landlord uses the following scheme for decision variables: 42) The landlord 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 = contractor works on kitchen tile x5 = contractor works on back door x6 = contractor works on back door x7 = contractor works on garage door x8 = contractor works on garage door What should the objective function be? A) Min Z = 2700x1 + 400x2 + 2500x3 + 1000x4 + 600x5 + 250x6 + 350x7 + 400x8 B) Min Z = 2700x1 - 400x2 + 2500x3 - 1000x4 + 600x5 - 250x6 + 350x7 - 400x8 C) Max Z = 100x1 + 100x2 + 80x3 + 80x4 + 15x5 + 15x6 + 20x7 + 20x8 D) Max Z = 100x1 - 100x2 + 80x3 - 80x4 + 15x5 - 15x6 + 20x7 - 20x8

48) 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 alternative sets of constraints ensures that no activities are duplicated at the ports of call? A) JS + JP + JH + JL + CS + CP + CH + CL + CTe + GS + GP + GH + GL + GTu ≤ 3 B) JS + JP + JH + JL = 1 CS + CP + CH + CL + CTe = 1 GS + GP + GH + GL + GTu = 1 C) JS + CS + GS ≤ 1 JP + CP + GP ≤ 1 JH + CH + GH ≤ 1 JL + CL + GL ≤ 1 D) JS + JP + JH + JL + CS + CP + CH + CL + CTe + GS + GP + GH + GL + GTu = 3

48) What is an appropriate constraint for this fast food vignette? A) 250T + 400B + 150M + 400C B) 4C + 1M + 0B + 4T ≤ 4 C) 2N + 4B + 4Q + 3E ≤ 400 D) 2.75N + 4B + 2Q + 3E

51) 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

54) A portion of the variable cells section of the sensitivity report in Excel appears in the table below. How many potential customers will be reached by the optimal advertising campaign? (look at the chart) A) 17.76 B) 8,900 C) 42,080 D) cannot be determined from the sensitivity report

58) If Xab = the production of product a in period b, then to indicate that the limit on production of the company's 3 products in period 2 is 400, we write: A) X32 ≤ 400. B) X21 + X22 + X23 ≤ 400. C) X12 + X22 + X32 ≤ 400. D) X12 + X22 + X32 ≥ 400.

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

63) Which of the following constraints best describes the relationship between the electronic Wall Street Journal subscription and the iPads? A) E - A = 0 B) E - A = 1 C) E - A ≤ 0 D) E - A ≤ 1

64) The poultry farmer has in mind the following levels for each of his metrics of interest: a plumage score greater than 75, fertilizer production greater than 80 ounces per week, temperament less than 100 decibels, and an appetite less than 160 ounces of layer pellets per week. When he runs his linear programming model, he discovers that his flock will consist entirely of Leghorn birds. He can picture the sad little faces of his children when he tells them that there will be no variety of birds gracing their front lawn this summer. Help him avoid the embarrassment by selecting a constraint that will ensure that there is some variety in his flock. A) 5L + 4C + 8B ≤ 160 B) 5L + 4C + 8B ≥ 160 C) C + B ≥ 5 D) L + C + B ≥ 5

67) 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

67) 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

69) 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

70) 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

71) 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.

78) The investor stipulates that stock 1 must not account for more than 35% of the number of shares purchased. Which constraint is correct? A) X1 ≤ 0.35 B) X1 = 0.35 (50000) C) X1 ≤ 0.35(X1 + X2 + X3) D) X1 = 0.35(X1 + X2 + X3)

78) What difference would it make to the solution if this scenario was modeled as a 0-1 problem instead of an integer model? A) There would not be any difference. B) The 0-1 model would result in a higher value for the objective function. C) The 0-1 model would result in a lower value for the objective function. D) The 0-1 model would be infeasible given the constraints that exist in the scenario.

85) 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

The Cruise 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 - 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. Site Rating Activity Cost Jamaica 3 snorkeling $100 Jamaica 1 party island $95 Jamaica 2 horseback ride $120 Jamaica 3 local cuisine $60 Cozumel 2 snorkeling $110 Cozumel 3 party island $55 Cozumel 1 horseback ride $70 Cozumel 2 local cuisine $90 Cozumel 3 tequila tasting $130 Grand Cayman 1 snorkeling $90 Grand Cayman 2 party island $60 Grand Cayman 3 horseback ride $110 Grand Cayman 1 local cuisine $130 Grand Cayman 3 turtle farm $95 (this is a chart in the document) (Note - data used in this test question should not be construed as vacation advice.) 46) What is an appropriate objective function for this vacation? A) Max Z = JS + JP + JH + JL + CS + CP + CH + CL + CTe + GS + GP + GH + GL + GTu B) Min Z = 100JS + 95JP + 120JH + 60JL + 110CS + 55CP + 70CH + 90CL + 130CTe + 90GS + 60GP + 110GH + 130GL + 95GTu C) Max Z = 3JS + 1JP + 2JH + 3JL + 2CS + 3CP + 1CH + 2CL + 3CTe + 1GS + 2GP + 3GH + 1GL + 3GTu D) Min Z = 3JS + 1JP + 2JH + 3JL + 2CS + 3CP + 1CH + 2CL + 3CTe + 1GS + 2GP + 3GH + 1GL + 3GTu

104) Kitty Kennels provides overnight lodging for a variety of pets. An attractive feature is the quality of care the pets receive, including well balanced nutrition. The kennel's cat food is made by mixing two types of cat food to obtain the "nutritionally balanced cat diet." The data for the two cat foods are as follows: (look at the chart) 104) Kitty Kennels wants to be sure that the cats receive at least 5 ounces of protein and at least 3 ounces of fat per day. What is the cost of this plan, and how much fat and protein do the cats receive?

Cost is $3.60, which uses 14 ounces of Meow Munch and 5.33 ounces of Feline Feed.

43) The landlord 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 = contractor works on kitchen tile x5 = contractor works on back door x6 = contractor works on back door x7 = contractor works on garage door x8 = contractor works on garage door Which of these constraints would not be appropriate for this scenario? A) 2700x1 + 400x2 + 2500x3 + 1000x4 + 600x5 + 250x6 + 350x7 + 400x8 ≤ 3000 B) 1x1 + 2x2 + 1.5x3 + 3x4 + 0.5x5 + 1x6 + 0.25x7 + 0.5x8 ≤ 4 C) x3 + x4 = 1 D) x1, x2, x3, x4, x5, x6, x7, x8 ≥ 0 and integer

45) Which of these answers is optimal? A) 120P, 100C, and 88B B) 130P, 88C and 100B C) 140P, 88C and 88B D) 150P and 400B

49) How many decision variables are in the LP formulation? A) 1 B) 2 C) 3 D) 4

50) Types of integer programming models are: A) total. B) 0-1. C) mixed. D) total, 0-1, and mixed

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

55) Which of these statements about the sensitivity report for the constraints is best?(look at the chart) A) Only $940 of the advertising budget is being spent on this campaign. B) The advertising campaign needs another $2,560 to reach the maximum number of customers. C) It is possible to reach enough customers by spending only $60. D) For every $1 increase in the budget, the ad campaign can reach twelve more customers.

57) 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.

58) 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

60) 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.

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

65) When the poultry farmer runs his linear programming model, he discovers that his flock will consist entirely of Leghorn birds. He studies his sensitivity report (copied below) and decides to write a constraint that requires two Cochin chickens to be selected. If the current optimal mix of breeds results in 160 eggs per week, which of the following statements is best? (look at the chart) A) The new weekly egg output will be 169. B) The new weekly egg output will be 162. C) The new weekly egg output will be 158. D) The new weekly egg output will be 153.

68) 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

68) 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

69) 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

70) 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

71) You have been asked to select at least 3 out of 7 possible sites for oil exploration. Designate each site as S1, S2, S3, S4, S5, S6, and S7. The restrictions are: Restriction 1. Evaluating sites S1 and S3 will prevent you from exploring site S7. Restriction 2. Evaluating sites S2 or S4 will prevent you from assessing site S5. Restriction 3. Of all the sites, at least 3 should be assessed. Assuming that Si is a binary variable, the constraint for the first restriction is: A) S1 + S3 + S7 ≥ 1. B) S1 + S3 + S7 ≤ 1. C) S1 + S3 + S7 = 2. D) S1 + S3 + S7 ≤ 2.

74) You have been asked to select at least 3 out of 7 possible sites for oil exploration. Designate each site as S1, S2, S3, S4, S5, S6, and S7. The restrictions are: Restriction 1. Evaluating sites S1 and S3 will prevent you from exploring site S7. Restriction 2. Evaluating sites S2 or S4 will prevent you from assessing site S5. Restriction 3. Of all the sites, at least 3 should be assessed. Assuming that Si is a binary variable, write the constraint(s) for the second restriction. A) S2 + S5 ≤ 1 B) S4 + S5 ≤ 1 C) S2 + S5 + S4 + S5 ≤ 2 D) S2 + S5 ≤ 1, S4 + S5 ≤ 1

77) What is the maximum value for the potluck? A) 13.28 B) 12.44 C) 15.02 D) 10.86

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

81) Suppose demand in sales center C drops to 400 units while demand in centers A and B both increase to 430. How does the problem formulation change? A) All of the constraints become less than or equal to constraints. B) Only the supply constraints become less than or equal to constraints. C) Only the demand constraints become less than or equal to constraints. D) The constraints do not change.

82) 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

99) Define the decision variables and objective function for this problem.

Define the decision variables: S1R = number of standard wheels produced in month 1 on regular time production S1O = number of standard wheels produced in month 1 on overtime production S2R = number of standard wheels produced in month 2 on regular time production S2O = number of standard wheels produced in month 2 on overtime production D1R = number of deluxe wheels produced in month 1 on regular time production D1O = number of deluxe wheels produced in month 1 on overtime production D2R = number of deluxe wheels produced in month 2 on regular time production D2O = number of deluxe wheels produced in month 2 on overtime production Y1 = number of standard wheels stored from month 1 to month 2. Y2 = number of deluxe wheels stored from month 1 to month 2. MIN 25 S1R + 37.5 S1O + 40 D1R + 60 D1O + 25 S2R + 37.5 S2O + 40 D2R + 60 D2O + 2 Y1 + 2 Y2

Saba conducts regular tours of his favorite city in the world, Paris. Each semester he selects among the finest students in the university and escorts them to the City of Lights. In addition to a world-class education on conducting business in Europe, he arranges a number of cultural outings for them to help them immerse themselves in all that France has to offer. He collects an extra $100 from each student for this purpose and limits his tour group to ten lucky individuals. Some of the events (and their prices) he proposes to the students include: Eiffel Tower visit, $40 per student, E Paris Sewer spelunking, $20 per student, S Half day passes to the Louvre, $60 per student, L Bon Beret tour, $50 per student, B So much to do and so little time! 103) What would the constraints be if the Eiffel Tower visit needed to take place at the same time as the half day at the Louvre and if students taking the Paris Sewer tour had to wear the special sanitary beret available only from the Bon Beret tour?

E + L ≤ 1 S - B ≤ 0

105) What is the full set of constraints if the following situations occur? The Eiffel Tower visit needed to take place at the same time has the half day at the Louvre. Students taking the Paris Sewer tour had to wear the special sanitary beret available only from the Bon Beret tour. Saba applies for university travel funds and supplements the students' accounts with an extra $30 each.

E + L ≤ 1 S - B ≤ 0 40E + 20S + 60L + 50B ≤ 130

122) What difference would it make to the solution if this scenario was modeled as a 0-1 problem instead of an integer model? Explain.

Each student would be bringing two different categories of items and the optimal answer would drop dramatically. The student would bring one of their best items from the original integer formulation and would then bring their second-best category. The meal would have a value of 10.86 and the assignments would be: Entrée Side Dessert Aaron 1 1 0 Alex 1 0 1 Dan 1 1 0 Erin 0 1 1 Julie 1 0 1 Kassie 1 1 0 Lindy 1 1 0 MacGregor 1 0 1 Marlene 0 1 1 Tracy 1 0 1

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

FALSE

10) The constraint x + y = z is written in standard form.

FALSE

11) In an unbalanced transportation model, supply does not equal demand, and supply constraints must have ≤ signs.

FALSE

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

FALSE

12) Transportation problems can have solution values that are non-integer and must be rounded.

FALSE

13) 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.

FALSE

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

FALSE

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

FALSE

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

FALSE

18) Fractional relationships among variables are considered standard form in a blending problem.

FALSE

19) Data envelopment analysis indicates which type of service unit makes the highest profit.

FALSE

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

FALSE

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

FALSE

22) Double-subscripted variables are required when there are two decision variables.

FALSE

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

FALSE

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

FALSE

24) 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.

FALSE

26) 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.

FALSE

3) When using a linear programming model to solve the diet problem, the objective is generally to maximize profit.

FALSE

6) In most media selection decisions, the objective of the decision maker is to minimize cost.

FALSE

6) 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.

FALSE

7) 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

8) A linear programming model of a media selection problem is used to determine the relative value of each advertising media.

FALSE

9) In a mixed integer model, all decision variables have integer solution values.

FALSE

103) Write the constraints for the total number of shirts of each style produced.

Form of constraint: number of shirts produced = (total yards used to make the shirt)/(yards/shirt) A = (XCA + XRA)/1 V = (XCV + XRV)/1.2 S = (XCS + XRS)/0.9 Standard form: A - XCA - XRA = 0 1.2 V - XCV - XRV = 0 0.9 S - XCS - XRS = 0

102) Write the constraints for the fabric requirements.

Form of constraints: Total yards used is greater than (or less than) total yards required × (% fabric required) shirts produced. XCA ≥ 0.6 A XVR ≤ 0.36V XSC ≤ 0.72 S

108) The poultry farmer discovers, much to his dismay, that the product mix that satisfies all of his constraints isn't really a mix of birds-it's a flock consisting of nothing but 32 Leghorns. (His constraints were a plumage score greater than 75, fertilizer production greater than 80 ounces per week, temperament less than 100 decibels, and an appetite less than 160 ounces of layer pellets per week.) Not only is his flock going to be a very one-note mix in terms of color, he is afraid that the gleaming white feathers and deafening noise will attract predators, or worse yet, his neighbors. He immediately embarks on a breeding program to develop a Super-Cochin that can lay 4.5 eggs per week with all other performance measures the same. His optimal solution is now 27.5 Leghorns and 5.625 Super-Cochins. Assuming that he is willing to settle for a flock that has 27 Leghorns and 5 Super Cochins, what is the weekly output of eggs and performance with respect to the constraints?

He should get (27 × 5) + (4.5 × 5) = 157.5 eggs per week The plumage score is now 126. The fertilizer output is 91 ounces per week, The temperament score is 94. The appetite is 155 ounces of layer pellets per week.

85) The production combination of 180 bags of pumpkin and 100 bags of chipotle-adobo is not feasible because one resource is exceeded. Which resource is exceeded and how much more is needed to produce this combination?

Herbs only, 20 ounces are needed

The Deadbeats 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 and 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 - 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. 91) Formulate an appropriate objective function for this scenario.

92) Formulate an appropriate model for this scenario.

If the variables are assigned as in the table: x1 = contractor works on wood floors x2 = landlord works on wood floors x3 = contractor works on kitchen tile x4 = contractor works on kitchen tile x5 = contractor works on back door x6 = contractor works on back door x7 = contractor works on garage door x8 = contractor works on garage door then an appropriate objective function will be: Max Z = 100x1 + 100x2 + 80x3 + 80x4 + 15x5 + 15x6 + 20x7 + 20x8 Subject to: x1 + x2 ≤ 1 x3 + x4 ≤ 1 x5 + x6 ≤ 1 x7 + x8 ≤ 1 2700x1 + 400x2 + 2500x3 + 1000x4 + 600x5 + 250x6 + 350x7 + 400x8 ≤ 3000 1x1 + 2x2 + 1.5x3 + 3x4 + 0.5x5 + 1x6 + 0.25x7 + 0.5x8 ≤ 4 x1, x2, x3, x4, x5, x6, x7, x8 are 0,1

94) I know it's hard to believe that his job as a management scientist doesn't comfortably keep him in Ferraris and caviar, but the insurance premiums on his ride are outrageous, and frankly it doesn't get good gas mileage in the city. Hence, the management scientist/landlord runs his model and receives this output. Provide an interpretation of exactly what will happen in the coming weeks. (look at document for a better chart than below) Cell Name Original Value Final Value Integer $G$4 wood floors contractor 1 0 Binary $H$4 wood floors landlord 1 1 Binary $G$5 kitchen tile contractor 1 1 Binary $H$5 kitchen tile landlord 1 0 Binary $G$6 back door contractor 1 0 Binary $H$6 back door landlord 1 0 Binary $G$7 garage door opener contractor 1 0 Binary $H$7 garage door opener landlord 1 0 Binary

It appears that the landlord/management scientist will tackle the wood floors himself and have a contractor install kitchen tile. This will take 3.5 weeks, leaving one half week free, and will cost $2900 out of the maximum $3,000 budget, leaving $100 - enough for beer and pizza, or at least pizza. It is somewhat ambiguous whether the landlord has four weeks to work with and the contractors have four weeks or whether the entire model's time constraint should have only four weeks - if we knew whether there were wood floors in the kitchen and two work groups would get in each other's way, then we could set up constraints to capture this situation.

109) A credit union wants to make investments in the following: (look at the chart) The firm will have $2,500,000 available for investment during the coming year. The following restrictions apply: Risk-free securities may not exceed 30% of the total funds, but must comprise at least 5% of the total. Signature loans may not exceed 12% of the funds invested in all loans (vehicle, consumer, other secured loans, and signature loans). Consumer loans plus other secured loans may not exceed the vehicle loans. Other secured loans plus signature loans may not exceed the funds invested in risk-free securities. How should the $2,500,000 be allocated to each alternative to maximize annual return? What is the annual return?

It is a picture in the notes** go find it to see the answer

123) Which student experiences the greatest loss of contribution to the objective function value if this scenario was modeled as a 0-1 problem instead of an integer model?

Lindy drops from two entrées and a 1.8 contribution to one entrée and a side, which is a 0.96 contribution, a reduction of 0.84.

88) What is the formulation for this problem?

MAX Z = $.20B + $.30C s.t. 6B + 3C ≤ 6600 1B + 1C ≤ 1400 2B + 4C ≤ 4800 C ≥ 400

83) What is the formulation for this problem?

MAX Z = 0. 5P + 0.6C + 0.4B s.t. 2P + 6C + 1.75B ≤ 1000 3P + 6C + 3.5B ≤ 2000 4P + 5C + 1.5B ≤ 1200

108) Write the objective function.

MIN Z = 1.25X1 + 1.50X2 + 1.00X3 + 2.000X4 + 750Y1 + 500Y2 + 1000Y3 + 300Y4

95) Write the formulation for this problem.

MIN Z = 5x1A + 6x1B + 7x1C + 6x2A + 9x2B + 8x2C + 7x3A + 4x3B + 6x3C s.t. x1A + x1B +x1C = 320 x2A + x2B +x2C = 420 x3A + x3B +x3C = 520 x1A + x2A +x3A = 400 x1B + x2B +x3B = 400 x1C + x2C +x3C = 460

95) The management scientist was planning to leave his actions up to the wisdom of his model, but before he could press "Solve" on his Excel spreadsheet, his wife weighed in on the project. This was only reasonable, as it was her house before they tied the knot. It has been her dream to move back into this cottage once the management scientist goes to his great reward. She insists that the back door and garage door components of this project happen. If the variables have been chosen as in the table, construct an objective function and constraints that meet the management scientist's bride's requests. x1 = contractor works on wood floors x2 = landlord works on wood floors x3 = contractor works on kitchen tile x4 = contractor works on kitchen tile x5 = contractor works on back door x6 = contractor works on back door x7 = contractor works on garage door x8 = contractor works on garage door

Max Z = 100x1 + 100x2 + 80x3 + 80x4 + 15x5 + 15x6 + 20x7 + 20x8 Subject to: x1 + x2 ≤ 1 x3 + x4 ≤ 1 x5 + x6 = 1 x7 + x8 = 1 2700x1 + 400x2 + 2500x3 + 1000x4 + 600x5 + 250x6 + 350x7 + 400x8 ≤ 3000 1x1 + 2x2 + 1.5x3 + 3x4 + 0.5x5 + 1x6 + 0.25x7 + 0.5x8 ≤ 4 x1, x2, x3, x4, x5, x6, x7, x8 are 0,1

93) Formulate an appropriate model for this scenario if the variables are assigned as in the table: x1 = contractor works on wood floors x2 = landlord works on wood floors x3 = contractor works on kitchen tile x4 = contractor works on kitchen tile x5 = contractor works on back door x6 = contractor works on back door x7 = contractor works on garage door x8 = contractor works on garage door

Max Z = 100x1 + 100x2 + 80x3 + 80x4 + 15x5 + 15x6 + 20x7 + 20x8 Subject to: x1 + x2 ≤ 1 x3 + x4 ≤ 1 x5 + x6 ≤ 1 x7 + x8 ≤ 1 2700x1 + 400x2 + 2500x3 + 1000x4 + 600x5 + 250x6 + 350x7 + 400x8 ≤ 3000 1x1 + 2x2 + 1.5x3 + 3x4 + 0.5x5 + 1x6 + 0.25x7 + 0.5x8 ≤ 4 x1, x2, x3, x4, x5, x6, x7, x8 are 0,1

111) What is an appropriate objective function for this scenario?

Max Z = 2.75N + 4B + 2Q + 3E

110) What is an appropriate objective function and constraints for this scenario?

Max Z = 2.75N + 4B + 2Q + 3E subject to: Cheese 2N + 4B + 4Q + 3E ≤ 400 Meat 0N + 1B + 2Q + 2E ≤ 150 Beans 4N + 0B + 0Q + 2E ≤ 400 Tortilla 3N + 4B + 1Q + 3E ≤ 250

105) How should the objective function read?

Max Z = 5L + 2C + 4.5B

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

Max Z = 5L + 2C + 4.5B 3L + 9C+ 6B >= 75 Subject to: 2L + 8C + 5B <= 100 3L + 2C + 4B >= 80 5L + 4C + 8B <= 160

118) Write the objective function for this problem.

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

116) You have been asked to select at least 3 out of 7 possible sites for oil exploration. Designate each site as S1, S2, S3, S4, S5, S6, and S7. The restrictions are: Restriction 1. Evaluating sites S1 and S3 will prevent you from exploring site S7. Restriction 2. Evaluating sites S2 or S4 will prevent you from assessing site S5. Restriction 3. Of all the sites, at least 3 should be assessed. Assuming that Si is a binary variable, write the constraint for the third restriction.

S1 + S2 + S3 +S4 + S5 + S6 + S7 ≥ 3

114) You have been asked to select at least 3 out of 7 possible sites for oil exploration. Designate each site as S1, S2, S3, S4, S5, S6, and S7. The restrictions are: Restriction 1. Evaluating sites S1 and S3 will prevent you from exploring site S7. Restriction 2. Evaluating sites S2 or S4 will prevent you from assessing site S5. Restriction 3. Of all the sites, at least 3 should be assessed. Assuming that Si is a binary variable, write the constraint for the first restriction.

S1 + S3 + S7 ≤ 2

100) Write the constraints for this problem.

S1R + S1O - Y1 = 1000 D1R + D1O - Y2 = 1200 S2R + S2O + Y1 = 750 D2R + D2O + Y2 = 1000 .5 S1R + .6 D1R ≤ 1000 .5 S1O + .6 D1O ≤ 500 .5 S2R + .6 D2R ≤ 1000 .5 S2O + .6 D12O ≤ 500

115) You have been asked to select at least 3 out of 7 possible sites for oil exploration. Designate each site as S1, S2, S3, S4, S5, S6, and S7. The restrictions are: Restriction 1. Evaluating sites S1 and S3 will prevent you from exploring site S7. Restriction 2. Evaluating sites S2 or S4 will prevent you from assessing site S5. Restriction 3. Of all the sites, at least 3 should be assessed. Assuming that Si is a binary variable, write the constraint(s) for the second restriction.

S2 + S5 ≤ 1, S4 + S5 ≤ 1

104) The tour group has three days remaining in Paris and the opportunity to do three cultural events. It is important to soak up as much culture as possible, so Saba decides to model this as a 0-1 integer program mandating that the group does three events. A couple of students object, not to the integer program, but to the set of cultural events that they have to choose from. They would rather have the option to do up to three events but perhaps only one or two and spend the rest of their time doing some "retail benchmarking." What was Saba's original constraint and how does that constraint change to cater to the whims of the students?

Saba's original constraint was E + L + S + B = 3, which directed the group to three tours. The new constraint is E + L + S + B ≤ 3, which allows for the possibility of no tours up to a maximum of three tours.

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

TRUE

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

TRUE

14) The divisibility assumption is violated by integer programming.

TRUE

15) One type of constraint in an integer program is a multiple-choice constraint.

TRUE

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

TRUE

18) A feasible solution to an integer programming problem is ensured by rounding down non-integer solution values.

TRUE

19) The feasible region in an integer programming graph is composed of a lattice of points.

TRUE

2) In a total integer model, all decision variables have integer solution values.

TRUE

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

TRUE

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

TRUE

25) Integer constraints are entered in the inequality dialog box within Excel's Solver routine.

TRUE

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

TRUE

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

TRUE

5) 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

7) 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

8) 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

94) The Excel LP model for this scenario shows the following sensitivity report for the constraints. Comment on the salient features. (look at the chart)

The budget has a shadow price of 12, meaning that for every $1 increase in budget, an additional 12 customers could be reached. Facebook's shadow price of 20 can be interpreted as an increase in 20 customers receiving the message for each additional Facebook posting up to 233 postings. Newspaper and Twitter are not in the model and thus have no opportunity cost in this formulation. The budget shadow price is robust, but that of Facebook is comparatively narrow.

100) The vacationing management scientist sat down at his computer keyboard, cracked his knuckles and decided on the scheme of location (J, C, or G) and excursion (S, P, H, L, Te or Tu), for his decision variables. He wrote constraints that read: JS + JP + JH + JL + CS + CP + CH + CL + CTe + GS + GP + GH + GL + GTu ≤ 3 JS + JP + JH + JL ≤ 1 CS + CP + CH + CL + CTe ≤ 1 GS + GP + GH + GL + GTu ≤ 1 What do these constraints accomplish in the model and which ones are necessary?

The first constraint limits the total number of excursions to 3. JS + JP + JH + JL + CS + CP + CH + CL + CTe + GS + GP + GH + GL + GTu ≤ 3 The second through the fourth constraints limit the excursions at each one of the ports to 1. JS + JP + JH + JL ≤ 1 CS + CP + CH + CL + CTe ≤ 1 GS + GP + GH + GL + GTu ≤ 1 The first constraint doesn't help the model and can be eliminated. If it were used in place of constraints 2 through 4, the model might suggest taking all three excursions at one port of call, which would be impossible.

97) The management scientist entered a trance-like state as he formulated his model. This state was interrupted by an integer-hating colleague, who insisted that the model should be run as a linear program rather than integer program. The management scientist sighed, relaxed the integer constraint, and ran the model, obtaining the following answer report. Provide a full interpretation and plan for action. Variable Cells Cell Name Original Value Final Value Integer $G$4 wood floors Contractor? 0 0 Contin $H$4 wood floors Landlord? 0 1 Contin $G$5 kitchen tile Contractor? 0 0.833 Contin $H$5 kitchen tile Landlord? 0 0.167 Contin $G$6 back door Contractor? 0 0.000 Contin $H$6 back door Landlord? 0 0 Contin $G$7 garage door opener Contractor? 0 1 Contin $H$7 garage door opener Landlord? 0 0 Contin Constraints Cell Name Cell Value Formula Status Slack $B$12 Total Time Weeks Contractor 4 $B$12<=$B$13 Binding 0 $E$10 Total Cost Contractor Price $3,000 $E$10<=$E$11 Binding 0 $I$4 wood floors Included? 1 $I$4<=$J$4 Binding 0 $I$5 kitchen tile Included? 1 $I$5<=$J$5 Binding 0 $I$6 back door Included? 2.78E-16 $I$6<=$J$6 Not Binding 1 $I$7 garage door opener Included? 1 $I$7<=$J$7 Binding 0

The landlord uses the entire budget, takes the entire four weeks and installs (or has the contractor install) the floors, garage door, and the kitchen tile, leaving only the back door off the improvement list. The kitchen tile project is split between the landlord, who does one-sixth of the work, and the contractor, who completes the remaining five-sixths. Although the model meets the constraints, this is not a practical solution in the real world. The management scientist should realize that moving to an integer solution within the LP feasible region will result in a feasible solution, albeit one with no guarantee of optimality. If the integer solution of wood floors and the garage door is chosen, there would be money and time both left over in the project budget, but the management scientist should reintroduce the integer constraint to confirm the best choice of action.

96) The management scientist was planning to leave his actions up to the wisdom of his model, but before he could press "Solve" on his Excel spreadsheet, his wife weighed in on the project. This was only reasonable, as it was her house before they tied the knot. It has been her dream to move back into this cottage once the management scientist goes to his great reward. She insists that the back door and garage door components of this project happen. After making these changes, the management scientist ran the model and obtained the following answer report. Provide a full interpretation. (Look at document for better charts) Variable Cells Cell Name Original Value Final Value Integer $G$4 wood floors Contractor? 0 0 Binary $H$4 wood floors Landlord? 1 1 Binary $G$5 kitchen tile Contractor? 1 0 Binary $H$5 kitchen tile Landlord? 0 0 Binary $G$6 back door Contractor? 0 1 Binary $H$6 back door Landlord? 0 0 Binary $G$7 garage door opener Contractor? 0 1 Binary $H$7 garage door opener Landlord? 0 0 Binary Constraints Cell Name Cell Value Formula Status Slack $B$12 Total Time Weeks 2.75 $B$12<=$B$13 Not Binding 1.25 $E$10 Total Cost $1,350 $E$10<=$E$11 Not Binding 1650 $I$4 wood floors Included 1 $I$4<=$J$4 Binding 0 $I$5 kitchen tile Included 0 $I$5<=$J$5 Not Binding 1 $I$6 back door Included 1 $I$6=$J$6 Binding 0 $I$7 gar door open Included 1 $I$7=$J$7 Binding 0 $G$4:$H$7= Binary

The landlord will be refinishing the wood floors and the contractor(s) will be tackling the garage door opener and back door installations. those projects will cost a total of $1350, leaving $1650 left in the budget. These projects will take 2.75 weeks out of the four weeks available. The landlord should be able to increase the monthly rent by $135 once these upgrades have been completed. The only upgrade not completed will be the kitchen tile.

93) The Excel LP model for this scenario shows the following sensitivity report for the variable cells. Comment on the salient features. (look at the chart)

The model recommends four Facebook postings and almost 14 radio spots which will reach 42,080 potential tourists. Forcing the two unchosen media would result in a drop of 1000 customers if newspaper entered the marketing mix and a drop of 800 customers if Twitter was required. The Facebook allowable decrease is of some concern among all shown as the decrease of 2 units is small by comparison to the other ranges shown for the newspaper, radio and Twitter channels.

112) The assistant manager had taken a management science class a few years before and while she knew enough to formulate the problem and implement it in Excel, the only sensitivity training she had ever received had to do with being more empathetic to the plight of her minimum wage workforce. Help her interpret the sensitivity report for the Nacholupa product as it appears below. (look at the chart)

The optimal product mix calls for 55 Nacholupas to be prepared at a sale price of $2.75. This amount of Nacholupas would be optimal if the price rose by 25 cents up to $3 or dropped by 11.4 cents down to $2.636.

121) What is the optimal solution to the potluck problem?

The potluck reaches a value of 15.02 with the students bringing these items. Student Entrée Aaron 2 entrées Alex 2 sides Josh 2 sides Erin 2 entrées Julie 2 desserts Kassie 2 entrées Lindy 2 entrées MacGregor 2 desserts Marlene 2 sides Tracy 2 desserts

97) Suppose demand in sales center C drops to 400 units. How does the problem formulation change?

The supply constraints become "less than or equal to" constraints and the total amount shipped to location C must now equal 400. All of the demand constraints are "equal to" constraints to force the model to ship product. MIN Z = 5x1A + 6x1B + 7x1C + 6x2A + 9x2B + 8x2C + 7x3A + 4x3B + 6x3C s.t. x1A + x1B +x1C ≤ 320 x2A + x2B +x2C ≤ 420 x3A + x3B +x3C ≤ 520 x1A + x2A +x3A = 400 x1B + x2B +x3B = 400 x1C + x2C +x3C = 400

82) Suppose demand in sales center C drops to 400 units. How does the problem formulation change and what is the optimal answer?

99) What is an appropriate objective function and constraints for this vacation?

Using the scheme of location (J, C, or G) and excursion (S, P, H, L, Te or Tu), the model should be expressed as: Max Z = 3JS + 1JP + 2JH + 3JL + 2CS + 3CP + 1CH + 2CL + 3CTe + 1GS + 2GP + 3GH + 1GL + 3GTu subject to: 100JS + 95JP + 120JH + 60JL + 110CS + 55CP + 70CH + 90CL + 130CTe + 90GS + 60GP + 110GH + 130GL + 95GTu <= 250 JS + JP + JH + JL ≤ 1 CS + CP + CH + CL + CTe ≤ 1 GS + GP + GH + GL + GTu ≤ 1 JS + CS + GS ≤ 1 JP + CP + GP <= 1 JH + CH + GH <= 1 JL + CL + GL <= 1 JS, JP, JH, JL, CS, CP, CH, CL, CTe, GS, GP, GH, GL, GTu are 0,1

The Cruise 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 - 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. Site Rating Activity Cost Jamaica 3 snorkeling $100 Jamaica 1 party island $95 Jamaica 2 horseback ride $120 Jamaica 3 local cuisine $60 Cozumel 2 snorkeling $110 Cozumel 3 party island $55 Cozumel 1 horseback ride $70 Cozumel 2 local cuisine $90 Cozumel 3 tequila tasting $130 Grand Cayman 1 snorkeling $90 Grand Cayman 2 party island $60 Grand Cayman 3 horseback ride $110 Grand Cayman 1 local cuisine $130 Grand Cayman 3 turtle farm $95 (Note - data used in this test question should not be construed as vacation advice.) 98) What is an appropriate objective function for this vacation?

Using the scheme of location (J, C, or G) and excursion (S, P, H, L, Te or Tu), the objective function should be expressed as: Max Z = 3JS + 1JP + 2JH + 3JL + 2CS + 3CP + 1CH + 2CL + 3CTe + 1GS + 2GP + 3GH + 1GL + 3GTu

101) The first day on the cruise was a "day at sea" meaning no port of call, and only the amenities onboard for amusement. Restless and uncomfortably full after seven trips through the buffet, the management scientist gambled away most of his vacation money at the onboard casino. The excursions would be a necessity, but now it became less important to maximize the joy of the excursions and more vital to get off the boat as cheaply as possible while still staying busy at the three ports of call. What is an appropriate objective function for this modified cruise vacation?

102) The first day on the cruise was a "day at sea" meaning no port of call, and only the amenities onboard for amusement. Restless and uncomfortably full after seven trips through the buffet, the management scientist gambled away most of his vacation money at the onboard casino. The excursions would be a necessity, but now it became less important to maximize the joy of the excursions and more vital to get off the boat as cheaply as possible while still staying busy at the three ports of call. What is an appropriate model for this modified cruise vacation?

Using the scheme of location (J, C, or G) and excursion (S, P, H, L, Te or Tu), the objective function should be expressed as: Min Z = 100JS + 95JP + 120JH + 60JL + 110CS + 55CP + 70CH + 90CL + 130CTe + 90GS + 60GP + 110GH + 130GL + 95GTu subject to: 100JS + 95JP + 120JH + 60JL + 110CS + 55CP + 70CH + 90CL + 130CTe + 90GS + 60GP + 110GH + 130GL + 95GTu ≤ 250 JS + JP + JH + JL = 1 CS + CP + CH + CL + CTe = 1 GS + GP + GH + GL + GTu = 1 JS + CS + GS ≤ 1 JP + CP + GP ≤1 JH + CH + GH ≤1 JL + CL + GL ≤1 JS, JP, JH, JL, CS, CP, CH, CL, CTe, GS, GP, GH, GL, GTu are 0,1

90) If Xij = the production of product i in period j, write an expression to indicate that the limit on production of the company's three products in period 2 is 400.

X12 + X22 + X32 ≤ 400

110) Write a constraint that will ensure that Weithoff purchases exactly two machines.

Y1 + Y2 + Y3 + Y4 = 2

33) 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

29) 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

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

conditional

30) "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

35) In a balanced transportation model, supply equals ________.

demand

29) 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

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

down

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

efficiency or productivity

89) For the production combination of 600 bear claws and 800 almond-filled croissants, how much flour and almond paste are remaining?

flour = 600 ounces, almond paste = 400 TS

101) Write the objective function.

max 30 A + 40 V + 36 S - 5C - 7R

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

media selection

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

minimize costs

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

mixed

32) 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

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

multiple-choice

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

mutually exclusive

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

one

27) 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

87) This represents what type of linear programming application?

product mix

32) Investment problems maximize ________.

return on investments

30) 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

37) 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

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

88) Consider a capital budgeting example with five projects from which to select. Let x1 = 1 if project a is selected, 0 if not, for a = 1, 2, 3, 4, 5. Projects cost $100, $200, $150, $75, and $300, respectively. The budget is $450. Write the appropriate constraint for the following condition: Choose no fewer than 3 projects.

x1 + x2 + x3 + x4 + x5 ≥ 3

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

x1 + x2 = 1

90) Write the appropriate constraint for the following condition: If project 1 is chosen, project 5 must not be chosen.

x1 + x5 ≤ 1

113) Solve the following integer linear program graphically. (There is a picture on the document for this one) MAX Z = 5x1 + 8x2 s.t. x1 + x2 ≤ 6 5x1 + 9x2 ≤ 45 x1, x2 ≥ 0 and integer

x1 = 0, x2 = 5, Z = 40 Note that feasible space lattice points have been shaded.

111) Max Z = x1 + 6x2 Subject to: 17x1 + 8x2 ≤ 136 3x1 + 4x2 ≤ 36 x1, x2 ≥ 0 and integer Find the optimal solution.

x1 = 0, x2 = 9, Z = 54

112) Max Z = 3x1 + 5x2 Subject to: 7x1 + 12x2 ≤ 136 3x1 + 5x2 ≤ 36 x1, x2 ≥ 0 and integer Find the optimal solution.

x1 = 12, x2 = 0, Z = 36

87) Consider the following integer linear programming problem: Max Z = 3x1 + 2x2 Subject to: 3x1 + 5x2 ≤ 30 5x1 + 2x2 ≤ 28 x1 ≤ 8 x1, x2 ≥ 0 and integer The solution to the linear programming formulation is: x1 = 5.714, x2 = 2.571. What is the optimal solution to the integer linear programming problem? State the optimal values of decision variables and the value of the objective function.

x1 = 4, x2 = 3, Z = 18

86) Consider the following integer linear programming problem: Max Z = 3x1 + 2x2 Subject to: 3x1 + 5x2 ≤ 30 4x1 + 2x2 ≤ 28 x1 ≤ 8 x1, x2 ≥ 0 and integer The solution to the linear programming formulation is: x1 = 5.714, x2 = 2.571. What is the optimal solution to the integer linear programming problem? State the optimal values of decision variables and the value of the objective function.

x1 = 6, x2 = 2, Z = 22

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

x1 = x2

119) Write the constraints for the three distribution centers.

x1A + x1B +x1C - 500y1 ≤ 0 x2A + x2B +x2C - 500y2 ≤ 0 x3A + x3B +x3C - 500y3 ≤ 0 The Potluck The study tour group had four weeks to recover from their digestive issues and put together their videos for the class assignment, which were to be shared at a final meeting over a potluck supper. There were ten students in the class and each was tasked with preparing two dishes to share with the rest of the group — either an entrée, a side, or a dessert. In order to make this meal optimal, their tour guide, who doubled as their management science professor, decided to model it as an integer program. He asked the students to rate themselves on their ability to prepare sweet or savory dishes and proteins or vegetables. Their ratings appear in the table. A reasonably balanced meal with plenty of choices calls for at least five entrées, at least six desserts, and at least six sides. The students agreed to bring two dishes apiece and breathlessly awaited the results of the optimization model. Entrée Side Dessert Aaron 0.70 0.41 0.68 Alex 0.56 0.52 0.03 Josh 0.40 0.73 0.39 Erin 0.70 0.62 0.66 Julie 0.18 0.16 0.32 Kassie 0.88 0.37 0.11 Lindy 0.90 0.06 0.44 MacGregor 0.43 0.20 0.99 Marlene 0.86 0.81 0.02 Tracy 0.83 0.01 0.96 120) Formulate this problem. Answer: Max Z = .7AaE + .56AlE + .4JoE + .7EE + .18JuE + .88KE + .90LE + .43McE + .86MrE + .83TE + .68AaD + .03AlD + .39JoD + .66ED + .32JuD + .11KD + .44LD + .99McD + .02MrD + .96 + .41AaS + .52AlS + .73JoS + .62ES + .16JuS + .37KS + .06LS + .20McS + .81MrS + .01TS subject to: AaE + AlE + JoE + EE + JuE + KE + LE + McE + MrE + TE ≥ 5 AaD + AlD + JoD + ED + JuD + KD + LD + McD + MrD + TD ≥ 6 AaS + AlS + JoS + ES + JuS + KS + LS + McS + MrS + TS ≥ 6 AaE + AaS + AaD = 2 AlE + AlS + AlD = 2 JoE + JoS + JoD = 2 EE + ES + ED = 2 JuE + JuS + JuD = 2 KE + KS + KD = 2 LE + LS + LD = 2 McE + McS + McD = 2 MrE + MrS + MrD = 2 TE + TS + TD = 2 all decision variables integer

89) Write the appropriate constraint for the following condition: If project 3 is chosen, project 4 must be chosen.

x3 - x4 ≤ 0

The Wiethoff Company has a contract to produce 10,000 garden hoses for a customer. Wiethoff has four different machines that can produce this kind of hose. Because these machines are from different manufacturers and use differing technologies, their specifications are not the same. 107) This problem requires two different kinds of decision variables. Clearly define each kind.

xa = the number of hoses produced on machine a; ya = 1 if machine a is used, 0 if not

109) Write a constraint to ensure that if machine 4 is used, then machine 1 will not be used.

y1 + y4 ≤ 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. 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. 117) 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

66) The poultry farmer has in mind the following levels for each of his metrics of interest: a plumage score greater than 75, fertilizer production greater than 80 ounces per week, temperament less than 100 decibels, and an appetite less than 160 ounces of layer pellets per week. Use this portion of the sensitivity report to evaluate the following statements: (look at the chart) A) The noise level around the farm should be over 60 decibels. B) The fertilizer generated will be 160 ounces per week. C) Layer pellets will be consumed at the rate of 96 ounces per week. D) The plumage score will be less than 40.

72) 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.

76) An appropriate part of the model would be: A) 15X1 + 47.25X2 + 110 X3 ≤ 50,000. B) MAX 15X1 + 47.25X2 + 110X3. C) X1 + X2 +X3 ≤ 50,000. D) MAX 50(15)X1 + 50 (47.25)X2 + 50 (110)X3.

79) Which of these is an appropriate constraint for the problem? A) x1A + x1B +x1C = 320 B) x1A + x2A +x3A = 320 C) x3A + x3B +x3C = 460 D) x1B + x2B +x3B = 420

86) What is the optimal product mix and resulting profit?

A profit of $235 is attainable if Artisanal Chips, Etc., produces 150 bags of pumpkin and 400 bags of basement flavored chips.

20) In a classic blending problem, revenue is maximized by subtracting cost from profit.

FALSE

44) Which of the following is not a feasible production combination? A) 128B and 128C B) 128C and 128P C) 128P and 128B D) 150P, 10C and 360B

47) Which of these is a decision variable for the LP formulation of this problem? A) cheese B) Nacholupa C) 400 D) $2.75

51) Which of the statements about this portion of the sensitivity report is best? Look at the chart A) Cheese costs more than meat. B) One additional pound of meat should be purchased if it can be acquired for $2 or less. C) There is both cheese and meat left over if the optimal product mix is produced. D) The shadow price of cheese can rise to 16.8167 before the right hand side changes.

53) Which of these is an appropriate constraint for this scenario? A) 5,000N + 3,000R + 700T + 200F ≤ 3,500 B) 500N + 250R + 125T + 15F ≤ 3,500 C) N + R + T + F ≥ 36 D) T ≤ 2,800

57) How should the entry for the Newspaper decision variable be interpreted?(look at the chart) A) The director should lower the newspaper advertising expense by $1,000 to reach the objective of 5,000 customers contacted. B) 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. C) If the director increased newspaper advertisement by 1,000, he would spend $1000 less than with the current campaign. D) It is possible to reach an almost infinite fewer number (10 to the 30th power) of customers by newspaper than by any other method.

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. 75) 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

41) The owner of Black Angus Ranch is trying to determine the correct mix of two types of beef feed, A and B, which cost 50 cents and 75 cents per pound, respectively. Five essential ingredients are contained in the feed, shown in the table below. The table also shows the minimum daily requirements of each ingredient. LOOK AT THE CHART The constraint for ingredient 3 is: A) .5A + .75B = 20. B) .3B = 20. C) .3B ≤ 20. D) .3B ≥ 20.

Agec 3413 test 2

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