Michael runs a specialty clothing store that sells collegiate sports apparel. One of his primary business opportunities involves selling sweatshirts for college football games. On September 1st, Michael’s store is delivered an order of 7,000 sweatshirts with a purchasing price of $20 per piece from his supplier. He plans to sell the sweatshirts for $35 per piece. 

Demand in September for sweatshirts follows a discrete uniform distribution with a minimum of 5,000 and a maximum of 10,000. At the end of September, if there are less than 5,000 sweatshirts in inventory, Michael places an order for 4,000 sweatshirts from his supplier. This order is delivered just in time on October 1st. Demand in October for sweatshirts follows a discrete uniform distribution with a minimum of 2,000 and a maximum of 6,000. At the end of October, if there are less than 4,000 sweatshirts in inventory, he places an order for 3,000 sweatshirts from his supplier. 

This order is delivered just in time on November 1st. During the rest of the college football season in November and December, demand for sweatshirts follows a discrete uniform distribution with a minimum of 1,000 and a maximum of 4,000. After the college football season ends, Michael plans to sell any remaining sweatshirts for $12 per piece. At this price, he believes demand for sweatshirts will follow a discrete uniform distribution with a minimum of 500 and a maximum of 4,000. At the end of December, all unsold sweatshirts are donated to homeless people shelters. Build a simulation model in Crystal Ball and run it for 1,000 replications to answer the following questions. 

a) Estimate the mean profit.

b) Estimate the probability that Michael can generate a profit larger than $100,000.