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Develop/calculate: payoff table, regret table, maintaining inventory/stock, and the decision alternative indicated by the maximum likelihood criterion.

1. A small, local, food store stocks kiwi fruit. In the past 50 weeks, the store has experienced the following weekly demand for mangoes:

Week! Demand Frequency
(number of mangoes) (weeks)

20 10
25 30
40 50
60 10

The food store buys the kiwi fruit from its supplier for $2.00 each and sells them for $3.00 each. Whatever is left unsold at the end of a week is discarded.

a. Develop the payoff table for this decision situation.
b. Develop the regret table for this decision situation.
c. Use the expected value criterion to determine the best (that is, the optimal) decision as regards the appropriate number of kiwi fruit to consistently stock.
d. Determine the decision alternative indicated by the maximum likelihood criterion.
e. Are the decisions of parts c and d the same? Whether they agree or not, explain why.
f. Assume that the probabilities given above are no longer valid. Determine the best decision using each of the following criteria:
1. Maximax.
2. Minimax regret
3. Hurwicz (condition of realism) with ct. = 0.3.
g. Determine the dollar amount the food store should be willing to pay to improve the decision (over the best decision found in part c above).

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