John Smith has been thinking of starting a gasoline station business. Smith owns

Question

John Smith has been thinking of starting a gasoline station business. Smith owns a piece of land near the intersection of two highways. But there are already a few gasoline stations nearby. He thinks that the annual returns will depend on two variables, the size of the station and a demand factor applicable to the area. After careful analysis, Smith develop the following payoff table: For example, if Smith constructs a small station and the demand is fair, he will realize a net return of $20,000. Answer the following questions. Show work. What is the solution from the point of view of: a. Perfect optimism (maximax)? b. Perfect pessimism (maximin)? c. Realism with alpha = 8? d. The criterion of conservatism (equal likelihood)? e. What is the minimax decision (criterion of regret)? f. On the basis of your calculations what would your decision be? Why? Explain.

Explanation / Answer

solution=

1.What is the solution from the point of view reviewed Criterion? On the basis of your calculations what would your decision be? Why? Explain.

a) Perfect Optimism–This selects the highest given value for the best case scenario of each alternative. In this instance the Gasoline Station Size selection would be VERY LARGE (with a GOOD DEMAND scenario) because $300,000 is the highest value

b) Perfect Pessimism–This selects the highest given value for the worst case scenario of each alternative. In this instance the Gasoline Station Size selection would be SMALL POOR DEMAND scenario) because $-10,000 is the highest of the lowest values.

c) Optimism at alpha = .8 – As shown below, using the given optimism coefficient, multiplying it against the best scenario for each selection, then multiplying (1-alpha ) against the worse scenario and adding the two results gives the Measure of Realism. The highest value is the best choice using this method, so VERY LARGE equipment should be selected.

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