3. A fitness center is considering an expansion. Three proposals are being considered: add new pool, add new equipment or add child center. The profits for three different customer responses for each proposal are shown in the table below:

Customer Response

High Moderate Low

Add New Pool 100,000 60,000 50,000

Add New Equipment 120,000 80,000 30,000

Add Child Center 120,000 70,000 60,000

For this problem:

(a) What is the optimal decision when using the maximax criterion? What is the payoff for it?

(b) What is the optimal decision when using the maximin criterion? What is the payoff for it?

(c) What is the optimal decision when using the minimax regret criterion? What is the payoff for it?

(d) What is the optimal decision using the Hurwicz’s criterion if α = 0.4? What is the payoff for it?

4. For the problem given in Question 3, assume that the probability of high customer response is 0.3, the probability of moderate customer response is 0.4, and the probability of low customer response is 0.3.

(a) Calculate the expected value of each decision alternative. What is your recommendation using the expected value criterion?

(b) Calculate the expected opportunity loss value of each decision alternative. What is your recommendation using the expected opportunity loss criterion?

(c) Calculate and interpret the value of perfect information.

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