The owner of a number of gasoline stations is planning to open a new station. The problem is to decide how large should be the station. The annual returns will depend on both the size of the station and a number of marketing factors related to the oil industry and the demand for gasoline. After a careful analysis, the owner has developed the following payoff table. (Negative signs refer to losses) Station Size Good Market ($) Fair Market ($) Poor Market ($) Small 50,000 20,000 30,000 Moderate 80,000 80,000 -20,000 Large 100,000 30,000 -40,000 Very Large 300,000 25,000 -160,000 A financial analyst hired by the owner has determined the probabilities of the future markets as follows: Good market, 0.2; fair market, 0.5; poor market, 0.3.
1. Using expected value criterion, determine the best decision.
a. Determine the maximum additional amount the company should be willing to pay to improve the decision.
b. Using maximum likelihood, determine the best decision.
c. Are the decisions of part 1 and part 1b the same? Whether they agree or not, explain why.