Exercise 2 Alicia Olsen, Logistics Manager at Nature's Table, needs to replenish her supply of strawberries. Her regular supplier of strawberries can provide as many cases as she wants. However, because these strawberries already are very ripe, Alicia will need to sell them tomorrow and then discard any that remain unsold. Alicia estimates that she will be able to sell 12. 13, 14. or 15 cases tomorrow. She can purchase the strawberries for $20 per case and sell them for $50 per case. Alicia needs to decide now how many cases to purchase. Alicia has checked the store's records on daily sales of strawberries. On this basis, she estimates that the prior probabilities are 0.15, 0.4, 0.30, and 0.15 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 Alicia Olsen purchase according to Bayes' decision rule? c. What is the maximum amount of money Alicia should be willing to spend to get more information about how many cases of strawberries she might be able to sell tomorrow? d. Alicia thinks she has the prior probabilities just about right for selling 12 cases and selling 15 cases, but is uncertain about the splitting of the probabilities for 13 cases and 14 cases. Perform a sensitivity analysis on the probabilities for 13 and 14 cases (without changing the prior probabilities for selling 12 cases and selling 15 cases) and comment on the implications of the result of the analysis