Jean Clark is the manager of the Midtown Saveway Grocery Store. She now needs to replenish her supply of strawberries. Her regular supplier can provide as many cases as she wants. However, because these strawberries already are very ripe, she will need to sell them tomorrow and then discard any that remain unsold. Jean estimates that she will be able to sell 10, 11, 12, or 13 cases tomorrow. She can purchase the strawberries for $3 per case and sell them for $8 per case. Jean now needs to decide how many cases to purchase. Jean has checked the store’s records on daily sales of strawberries. On this basis, she estimates that the prior probabilities are 0.2, 0.4, 0.3, and 0.1 for being able to sell 10, 11, 12, and 13 cases of strawberries tomorrow.

a. Develop a decision analysis formulation of this problem by identifying the decision alternatives, the states of nature, and the payoff table.

b. How many case of strawberries should Jean purchase if she uses the maximin payoff criterion.

c. How many cases should be purchased if she uses the maximum likelihood criterion?

d. How many cases should be purchased according to Bayes’ decision rule?

e. Jean thinks she has the prior probabilities just about right for selling 10 cases and selling 13 cases, but is uncertain about how to split the prior probabilities for 11 cases and 12 cases. Reapply Bayes’ decision rule when the prior probabilities of 11 and 12 cases are (i) 0.2 and 0.5, (ii) 0.3 and 0.4, and (iii) 0.5 and 0.2.