You run a food bar in UCLA Ackerman, and you sell chocolate croissants for breakfast. Your daily demand for chocolate croissants is on average 50, with a standard deviation of 8. The unit cost of a croissant is $0.70, and you sell at a unit price of $3.00. The refrigerated chocolate croissant must be consumed within 7days (one week) after purchased from your supplier, so you dispose leftover inventory and purchase fresh croissants once every week. Assume the demand in each of the seven days is independently distributed. (The z-table for normal distribution is attached.)

(a) What is the optimal weekly purchase quantity for the chocolate croissant? What is average inventory?

A student leader, Mark, came to you one day and told you that Anderson School would hold a special event next Thursday morning, and there would be additional demand for the chocolate croissant on that day. Mark wants to reserve a certain amount of croissant from you and sell in the special event at the regular price. You decide to give him a discounted price of $2.00. Since the croissants won’t be refrigerated in that event, any leftovers have to be disposed. Because Mark is an MBA, he decides on the reserved quantity according to the Newsvendor model.

(b) If you want to maximize the total expected profit that would be obtained by you and Mark, what should be your buyback price for the leftovers given your discounted selling price of $2.00?

(c) What is your expected profit given all the parameters in part b? (hint: use Loss function).