a. A car rental agency faces the decision of buying a fleet of cars, all of which will be the same size. It can purchase a fleet of small cars, medium cars, or large cars. The smallest cars are the most fuel- efficient and the largest cars use the most fuel. One of the problems for the decision-makers is that they do not know whether the price of fuel will increase or decrease in the near future. If the price increases, the small cars are likely to be most popular. If the price decreases, customers may demand the larger cars. Following is a decision table with these decision alternatives, the states of nature, the probabilities, and the payoffs. Use this information to determine the EMV for this problem.b. The decision-makers have an opportunity to purchase a forecast of the world oil markets that has some validity in predicting gasoline prices. The following matrix gives the probabilities of these forecasts being correct for various states of nature. Use this information to revise the prior probabilities and recompute the EMV on the basis of sample information. What is the expected value of sample information for this problem? Should the agency decide to buy the forecast?

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Decision Alternative Small Cars Medium Cars Large Cars State of Nature Fuel Decrease (0.60) Fuel Increase (0.40) -$225 $125 $350 $425 -$150 -$400