Michael Abrams runs a specialty clothing store that sells collegiate sports apparel. One of his primary business opportunities involves selling custom screenprinted sweatshirts for college football bowl games. He is trying to determine how many sweatshirts to produce for the upcoming Tangerine Bowl game. During the month before the game, Michael plans to sell hissweatshirts for $25 a piece. At this price, he believes the demand for sweatshirts will be triangularly distributed with a minimum demand of 10,000, maximum demand of 30,000 and a most likely demand of 18,000. During the month after the game, Michael plans to sell any remaining sweatshirts for $12 a piece. At this price, he believes the demand for sweatshirts will be triangularly distributed with a minimum demand of 2,000, maximum demand of 7,000, and a most likely demand of 5,000. Two months after the game, Michael plans to sell any remaining sweatshirts to a surplus store that has agreed to buy up to 2,000 sweatshirts for a price of $3 per shirt. Michael can order custom screenprinted sweatshirts for $8 a piece in lot sizes of 3,000.

a. On average, how much profit would Michael earn if he orders 18,000 sweatshirts?
b. How many sweatshirts should he order if he wants to maximize his expected profit