1. An investor is considering two investment options, one high risk and one low risk. The returns given performance parameters of the U.S. gross domestic product are given below in hundreds of dollars per five thousand dollars invested.

GDP Growth

Under -1% -1% to +2% Over -2%

Low Risk \[{{d}_{1}}\] 0 \[\] 4 6

High Risk \[{{d}_{2}}\] \[-2\] 3 7

1. Use the optimistic method to determine the optimal investment.
2. Use the conservative method to determine the optimal investment.
3. Use the minimum/maximum regret method to determine the optimal investment.
4. Suppose \[P({{s}_{1}})=0.15\] , \[P({{s}_{2}})=0.25\] , and \[P({{s}_{3}})=0.60\] Use the expected value method to determine the optimal investment.
5. Find the expected value of perfect information. If a consultant offers her services to the investor to do further research on determining the best investment for $500, should the investor accept the offer? Why?

2) An airline wants to begin operations in a new city. Two cities, A and B, are being considered. The airline will locate in the city whose airport has the lowest landing fees. These are determined by demand. The cost, in tens of thousands of dollars per year, is summarized in the table below.

DEMAND

High Medium Low

City A \[{{d}_{1}}\] 28 27 23

City B \[{{d}_{2}}\] \[\] 27 26 25

1. Use the optimistic method to determine the optimal location.
2. Use the conservative method to determine the optimal location.
3. Use the minimum/maximum regret method to determine the optimal location.
4. Suppose the \[p({{s}_{1}})=0.60{{,}_{{}}}p({{s}_{2}})=0.30\] and \[p({{s}_{3}})=0.10\] . Use the expected value method to determine the optimal location.

3) A business is considering two sizes for its new warehouse: small and large. An analysis of the profits realized given two states of demand, low and high, are summarized in the table below. Figures are in tens of thousands of dollars per month.

Demand

High Low

Size

Small \[{{d}_{1}}\] 95 60

Large \[{{d}_{2}}\] 115 45

1. Suppose \[p=P({{s}_{1}}).\] Use graphical sensitivity analysis to determine the range of values of p that each decision alternative is optimal.

Use the decision tree to answer the following questions.

1. What is the optimal decision if the study is not used? Use the expected value method.
2. Find the expected value of perfect information.
3. What is the optimal decision strategy if the study is used?
4. Suppose the cost of the study is estimated to be $7,250. Should it be conducted? Why or why not?
5. Find the efficiency of sample information.

4) Consider the model on the following page. The Management Scientist output is directly below it. Use it to answer the questions which follow. Use the 100% rule for objective function coefficients and right hand side ranges where appropriate. Do not run the changed model. Assume that any changes given in a of the problem are the only changes being made in the model.

1. What is the optimal solution? What are the corresponding values of the decision variables?
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2. Suppose the coefficient of E is changed to 71. Will the optimal solution change? Why or why not?
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3. Suppose the coefficient of S is changed to 86. Will the optimal solution change? Why or why not?
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4. Suppose the coefficient of E is changed to 59, that of S 101 to and that of D to 145. Will the optimal solution change? Why or why not?
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5. Suppose the coefficient of E is changed to 70, that of S to 91 and that of D to 147. Will the optimal solution change? Why or why not?
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6. Which resource is not completely used?
7. Suppose the number of fan motors is increased by 45. By how much will quality air’s profits change?
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8. Suppose the number of available cooling coils is increased by 70. By how much will Quality Air’s profits increase?
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9. Suppose the number of available fan motors is changed to 170, that of cooling coils to 365 and the number of available manufacturing hours to 2270. Will the dual prices of those constraints change? Why or why not?
10. Suppose number of available fan motors is changed to 220, the number of cooling coils to 275 and the number of available manufacturing hours to 2625. Will the dual prices of those constraints change? Why or why not?

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