# A sweatshirt supplier is trying to decide how many sweatshirts to print for the upcoming NCAA basketball

## Question:

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 interest in the tournament is at its highest) has the distribution shown in the file P15_14.xlsx. The residual demand, after the sweatshirts have been put on sale, has the distribution also shown in this file. 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. Use @RISK to analyze the sweatshirt situation. Using the discrete distributions given in the problem, what are the mean and the standard deviation of the profit to the sweatshirt supplier should he decide to print 11,000 sweatshirts? Round your answers to the nearest whole dollar, if necessary.

Demand distribution at regular price | Demand distribution at reduced price | ||||||||||

Demand | Probability | Demand | Probability | ||||||||

7 | 0.05 | 2 | 0.20 | ||||||||

8 | 0.10 | 3 | 0.30 | ||||||||

9 | 0.25 | 4 | 0.20 | ||||||||

10 | 0.30 | 5 | 0.15 | ||||||||

11 | 0.20 | 6 | 0.10 | ||||||||

12 | 0.10 | 7 | 0.05 |

Mean | $ |

Standard deviation | $ |

Repeat the simulation using normal distributions instead. Assume that the regular demand is normally distributed with mean 9800 and standard deviation 1300, and that the demand at the reduced price is normally distributed with mean 3800 and standard deviation 1400. What are now the mean and the standard deviation of the profit to the sweatshirt supplier should he still decide to print 11,000 sweatshirts? Round your answers to the nearest whole dollar, if necessary.

Mean | $ |

Standard deviation | $ |

Compare the @RISK simulation results obtained using discrete and normal distributions. Are they similar or not? Explain.

The results from @RISK's Define Distributions are that the mean and standard deviation for these discrete distributions are Select very close to distinct from item 5 those for the normal distributions.

Repeat the last simulation that uses normal distributions with sweatshirt production quantities ranging from 11,000 to 13,000 at 250 increments. How many sweatshirts should the sweatshirt supplier print for the upcoming NCAA basketball championships if he wants to maximize mean profit?

**Related Book For**

## Statistics Principles and Methods

ISBN: 978-0470904114

7th edition

Authors: Richard A. Johnson, Gouri K. Bhattacharyya