Problem 1.

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, 13, or 14 cases tomorrow. She can purchase the strawberries for $6 per case and sell them for $17 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 demand probability distribution is

Demand (cases) - 10 11 12 13 14

Probability - 0.09 0.18 0.16 0.24 0.33

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

(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 the expected payoff decision rule?

(e) What is EVPI in this case?

(f) How many cases should be purchased according to the minimax regret decision rule?

(g) If Jean's utility function is given by u(t)=√t, what is her optimal decision?