Discussion 1
In your own words, explain how to obtain the “expected value of perfect information” for any payoff table, which has probabilities associated with each state of nature. Then, provide an example, drawing from any of the payoff tables in Problems 1-17 in the back of Chapter 12. If no probabilities are given for the states of nature, then assume equal likelihood.
Problems
1. A farmer in Iowa is considering either leasing some extra land or investing in savings certificates at the local bank. If weather conditions are good next year, the extra land will give the farmer an excellent harvest. However, if weather conditions are bad, the farmer will lose money. The savings certificates will result in the same return, regardless of the weather conditions. The return for each investment, given each type of weather condition, is shown in the following payoff table:
Weather
Decision Good Bad
Lease land $90,000 $−40,000
Buy savings certificate 10,000 10,000
2. Select the best decision, using the following decision criteria:
1. Maximax
2. Maximin
3. The owner of the Burger Doodle Restaurant is considering two ways to expand operations: open a drive-up window or serve breakfast. The increase in profits resulting from these proposed expansions depends on whether a competitor opens a franchise down the street. The possible profits from each expansion in operations, given both future competitive situations, are shown in the following payoff table:
Competitor
Decision Open Not Open
Drive-up window $−6,000 $20,000
Breakfast 4,000 8,000
4. Select the best decision, using the following decision criteria.
1. Maximax
2. Maximin
5. Stevie Stone, a bellhop at the Royal Sundown Hotel in Atlanta, has been offered a management position. Although accepting the offer would assure him a job if there was a recession, if good economic conditions prevailed, he would actually make less money as a manager than as a bellhop (because of the large tips he gets as a bellhop). His salary during the next 5 years for each job, given each future economic condition, is shown in the following payoff table:
Economic Conditions
Decision Good Recession
Bellhop $120,000 $60,000
Manager 85,000 85,000
6. Select the best decision, using the following decision criteria.
1. Minimax regret
2. Hurwicz (α = .4)
3. Equal likelihood
7. Brooke Bentley, a student in business administration, is trying to decide which management science course to take next quarter—I, II, or III. “Steamboat” Fulton, “Death” Ray, and “Sadistic” Scott are the three management science professors who teach the courses. Brooke does not know who will teach what course. Brooke can expect a different grade in each of the courses, depending on who teaches it next quarter, as shown in the following payoff table:
Professor
Course Fulton Ray Scott
I B D D
II C B F
III F A C
8. Determine the best course to take next quarter, using the following criteria.
1. Maximax
2. Maximin
9. A farmer in Georgia must decide which crop to plant next year on his land: corn, peanuts, or soybeans. The return from each crop will be determined by whether a new trade bill with Russia passes the Senate. The profit the farmer will realize from each crop, given the two possible results on the trade bill, is shown in the following payoff table:
Trade Bill
Crop Pass Fail
Corn $35,000 $8,000
Peanuts 18,000 12,000
Soybeans 22,000 20,000
10. Determine the best crop to plant, using the following decision criteria.
1. Maximax
2. Maximin
3. Minimax regret
4. Hurwicz (α = .3)
5. Equal likelihood
11. A company must decide now which of three products to make next year to plan and order proper materials. The cost per unit of producing each product will be determined by whether a new union labor contract passes or fails. The cost per unit for each product, given each contract result, is shown in the following payoff table:
Contract Outcome
Product Pass Fail
1 $7.50 $6.00
2 4.00 7.00
3 6.50 3.00
12. Determine which product should be produced, using the following decision criteria.
1. Minimin
2. Minimax
13. The owner of the Columbia Construction Company must decide between building a housing development, constructing a shopping center, and leasing all the company’s equipment to another company. The profit that will result from each alternative will be determined by whether material costs remain stable or increase. The profit from each alternative, given the two possibilities for material costs, is shown in the following payoff table:
Material Costs
Decision Stable Increase
Houses $ 70,000 $30,000
Shopping center 105,000 20,000
Leasing 40,000 40,000
14. Determine the best decision, using the following decision criteria.
1. Maximax
2. Maximin
3. Minimax regret
4. Hurwicz (α = .2)
5. Equal likelihood
15. A local real estate investor in Orlando is considering three alternative investments: a motel, a restaurant, or a theater. Profits from the motel or restaurant will be affected by the availability of gasoline and the number of tourists; profits from the theater will be relatively stable under any conditions. The following payoff table shows the profit or loss that could result from each investment:
Gasoline Availability
Investment Shortage Stable Supply Surplus
Motel $−8,000 $15,000 $20,000
Restaurant 2,000 8,000 6,000
Theater 6,000 6,000 5,000
16. Determine the best investment, using the following decision criteria.
1. Maximax
2. Maximin
3. Minimax regret
4. Hurwicz (α = .4)
5. Equal likelihood
17. A television network is attempting to decide during the summer which of the following three football games to televise on the Saturday following Thanksgiving Day: Alabama versus Auburn, Georgia versus Georgia Tech, or Army versus Navy. The estimated viewer ratings (millions of homes) for the games depend on the win–loss records of the six teams, as shown in the following payoff table:
Number of Viewers (1,000,000s)
Game Both Teams Have Winning Records One Team Has Winning Record; One Team Has Losing Record Both Teams Have Losing Records
Alabama vs. Auburn 10.2 7.3 5.4
Georgia vs. Georgia Tech 9.6 8.1 4.8
Army vs. Navy 12.5 6.5 3.2
Discussion 2
Select one (1) of the following topics for your primary discussion posting:
•Identify the part of setting up a simulation in Excel that you find to be the most challenging, and explain why. Identify resources that can help you with that.
•Explain how simulation is used in the real world. Provide a specific example from your own line of work (Biotech/Pharmaceutical), or a line of work that you find particularly interesting.