1.Michelle Abrams runs a specialty clothing store that sells collegiate sports apparel. One of her primary business opportunities involves selling custom screen printed sweatshirts for college football bowl games. She is trying to determine how many sweatshirts to produce for the upcoming Tangerine Bowl game. During the month before the game, Michelle plans to sell his sweatshirts for $30 each. At this price, she believes the demand for sweatshirts will be normally distributed with mean 7,000 and standard deviation 1,500. During the month after the game, Michelle plans to sell any remaining sweatshirts for $12 each. At this price, she believes the demand for sweatshirts will be uniformly distributed with a minimum demand of 300, and a maximum demand of 1,000. Two months after the game, Michelle plans to sell any remaining sweatshirts to a surplus store that has agreed to buy up to 1,500 sweatshirts for a price of $3 per shirt. Michelle can order custom screen printed sweatshirts for $10 per sweatshirt in lot sizes of 200.

a.Determine the average profit that Michelle would earn if she orders 10,000 sweatshirts. (21pts)

b.Find the probability that Michelle's profit would be less than or equal to $100,000 if she orders 10,000 sweatshirts. (6 points)

c.How many sweatshirts would you recommend Michelle order to maximize average profit? (7 points)