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 12, 13, 14, or 15 cases tomorrow. She can purchase the strawberries for $7 per case and sell them for $18 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 0.1, 0.3, 0.4, and 0.2 for being able to sell 12, 13, 14, and 15 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 cases of strawberries should Jean purchase if she uses the maximin payoff criterion?
(c) How many cases should be purchased according to 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 12 cases and selling 15 cases, but is uncertain about how to split the prior probabilities for 13 cases and 14 cases. Reapply Bayes’ decision rule when the prior probabilities of 13 and 14 cases are (i) 0.2 and 0.5, (ii) 0.4 and 0.3, and (iii) 0.5 and 0.2.