Robert Man is the manager of the Midtown Safeway Grocery Store. He now needs to replenish his supply of strawberries. He regular supplier can provide as many cases as he wants. However, because these strawberries already are very ripe, he will need to sell them tomorrow and then discard any that remain unsold. Robert estimates that he will be able to sell 10, 11, 12, or 13 cases tomorrow. He can purchase the strawberries for $3 per case and sell them for $8 per case. Robert now needs to decide how many cases to purchase. Robert has checked the store’s records on daily sales of strawberries. On this basis, he 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.

1. What are decision variables and what are the states of nature in this problem?

2. Draw and upload the payoff table for this problem.

3. If Robert wants to follow the maximin criterion, what should he do and why?

4. How many cases should Robert order if he follows the maximum likelihood criterion? Why?

5. How many cases should Robert order if he follows Bayes' decision rule and why?

6. What's the most Robert should be willing to spend to get more information about how many cases of strawberries he might be able to sell tomorrow?