Fenton and Farrah Friendly, husband-and-wife car dealers, are soon going to open a new dealership. They have three offers: from a foreign compact car company, from a U.S.- producer of full-sized cars, and from a truck company. The success of each type of dealership will depend on how much gasoline is going to be available during the next few years. The profit from each type of dealership, given the availability of gas, is shown in the following payoff table: Gasoline Avalability Dealership Shortage 0.6 Surplus 0.4 Compact Cars $300,000 $150,000 Full-sized cars -100,000 600,000 Trucks 120,000 170,000 a) Determine which type of dealership the couple should purchase. b) Construct a decision tree for this problem’s decision and indicate the best decision. The Friendlys are considering hiring a petroleum analyst to determine the future availability of gasoline. The analyst will report that either a shortage or a surplus will occur. The probability that the analyst will indicate a shortage, given that a shortage actually occurs is .90; the probability that the analyst will indicate a surplus, given that a surplus actually occurs is .70. c) Determine the decision strategy the Friendlys should follow, the expected value of this strategy, and the maximum amount the Friendlys should pay for the analyst’s services. d) Compute the efficiency of the sample information for the Friendly car dealership.
Fenton and Farrah Friendly, husband-and-wife car dealers, are soon going to open a new dealership. They have three offers: from a foreign compact car company, from a U.S.- producer of full-sized cars, and from a truck company. The success of each type of dealership will depend on how much gasoline is going to be available during the next few years. The profit from each type of dealership, given the availability of gas, is shown in the following payoff table:
| Gasoline Avalability | ||
| Dealership |
Shortage |
Surplus 0.4 |
| Compact Cars | $300,000 | $150,000 |
| Full-sized cars | -100,000 | 600,000 |
| Trucks | 120,000 | 170,000 |
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a) Determine which type of dealership the couple should purchase.
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b) Construct a decision tree for this problem’s decision and indicate the best decision.
The Friendlys are considering hiring a petroleum analyst to determine the future availability of gasoline. The analyst will report that either a shortage or a surplus will occur. The probability that the analyst will indicate a shortage, given that a shortage actually occurs is .90; the probability that the analyst will indicate a surplus, given that a surplus actually occurs is .70.
c) Determine the decision strategy the Friendlys should follow, the expected value of this strategy, and the maximum amount the Friendlys should pay for the analyst’s services.
d) Compute the efficiency of the sample information for the Friendly car dealership.
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