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Question
NARRBEGIN: SA_93_95After Michigan State University reached the final four in the 2000 NCAA Basketball Tournament, a sweatshirt supplier in Lansing is trying to decide how many sweatshirts to print for the upcoming championships. The final four teams (Michigan State, Florida, Wisconsin, and North Carolina) have emerged from the quarterfinal round, and there is a week left until the semifinals, which are then followed in a couple of days by the finals. Each sweatshirt costs $12 to produce and sells for $24. However, in three weeks, any leftover sweatshirts will be put on sale for half price, $12. The supplier assumes that the demand (in thousands) for his sweatshirts during the next three weeks, when interest is at its highest, follows the probability distribution shown in the table below. The residual demand, after the sweatshirts have been put on sale, also has the probability distribution shown in the table below. The supplier realizes that every sweatshirt sold, even at the sale price, yields a profit. However, he also realizes that any sweatshirts produced but not sold must be thrown away, resulting in a $12 loss per sweatshirt.
| Demand distribution at regular price | Demand distribution at reduced price | |||
| Demand | Probability | Demand | Probability | |
| 7 | 0.05 | 2 | 0.2 | |
| 8 | 0.1 | 3 | 0.3 | |
| 9 | 0.25 | 4 | 0.2 | |
| 10 | 0.3 | 5 | 0.15 | |
| 11 | 0.2 | 6 | 0.1 | |
| 12 | 0.1 | 7 | 0.05 | |
Use simulation to analyze the supplier's problem. Determine how many sweatshirts he should produce to maximize the expected profit.
Answer
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