Problem 1:

A sweatshirt supplier is trying to decide how many sweatshirts to print for the upcoming NCAA basketball championships. The final four teams have emerged from the quarterfinal round, and there is now a week left until the semifinals, which are then followed in a couple of days by the finals. Each sweatshirt costs $10 to produce and sells for $25. However, in three weeks, any leftover sweatshirts will be put on sale for half price, $12.50. The supplier assumes that the demand for his sweatshirts during the next three weeks (when the interest in the tournament is at its highest) has the following distribution (see below table). The residual demand, after the sweatshirts have been put on sale, has the distribution also shown in the below table.

Demand distribution at regular price		Demand distribution at reduced price
Demand#	Probability		Demand#	Probability
7000	0.05		2000	0.20
8000	0.10		3000	0.30
9000	0.25		4000	0.20
10000	0.30		5000	0.15
11000	0.20		6000	0.10
12000	0.10		7000	0.05

The supplier, being a profit maximizer, realizes that every sweatshirt sold, even at the sale price, yields a profit. However, he also realizes that any sweatshirts produced but not sold (even at the sale price) must be thrown away, resulting in a $10 loss per sweatshirt. As you would have guessed, do NOT use @RISK to analyze this problem. [3 X 15 = 45 Points]

1. Analyze the supplier's problem with a simulation model using 1000 iterations. Specifically, compute all summary measures including a 95% confidence interval around the mean profit.
2. Also develop a data table for average profit as function of order quantity.
3. What order quantity provides the best profit?

A B C D E F G H 1 Sweatshirts for NCAA tournament blank column blank column 2 blank row 3 Inputs value Distribution of demand at regular price Distribution of demand at sale price 4 Unit cost $10 Cum Prob Demand Probability Cum Prob Original price Demand Probability $25 7000 0.05 2000 0.20 6 Sale price $12.50 8000 0.10 3000 0.30 7 end data 9000 0.25 4000 0.20 8 10000 0.30 5000 0.15 9 1 1000 0.20 6000 0.10 10 Decision variable 12000 0.10 7000 0.05 11 Order quantity (trial value) end data end data Problem 12.6