Jean Clark is the manager of the Midtown Safeway 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.
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. (NOTE: You can draw the table either using software (e.g., Microsoft Paint, PowerPoint) or on a piece of paper and take a picture.)
3. If Jean wants to follow the maximin criterion, what should she do and why?
4. How many cases should Jean order if she follows the maximum likelihood criterion? Why?
5. How many cases should Jean order if she follows Bayes' decision rule and why?
6. What's the most Jean should be willing to spend to get more information about how many cases of strawberries she might be able to sell tomorrow?