The Fish House (TFH) in Norfolk, Virginia, sells fresh fish and seafood. TFH receives daily shipments of farm-raised trout from a nearby supplier. Each trout costs $2.75 and is sold for $4.95. To maintain its reputation for freshness, at the end of the day, TFH sells any leftover trout to a local pet food manufacturer for $1.60 each. Daily demand for the trout is an integer between 10 and 20 (inclusive). The owner of TFH wants to determine how many trout to order each day.
1. Construct a payoff table for this [10 points]
2. What purchase quantity should be made according to the maximax decision rule? [5 points]
3. What purchase quantity should be made according to the maximin decision rule? [5 points]
4. What purchase quantity should be made according to the Laplace (equally-likely) decision rule? [5 points]
5. What purchase quantity should be made according to the minimax regret decision rule? [10 points]
Historically, the daily demand for trout is given in the following table.
| Demand | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
| Probability | 0.03 | 0.05 | 0.07 | 0.11 | 0.13 | 0.15 | 0.18 | 0.11 | 0.09 | 0.06 | 0.02 |
6. What purchase quantity should be made to maximize the expected daily profit? [5 points]
7. How much should the owner of TFH be willing to pay to obtain a daily demand forecast that is 100% accurate? [10 points]