1. Ali Derimod owns several retail fur stores in Turkey. In the spring of each year, he must decide on the number of each type of fur coat to order from his manufacturing supplier for the upcoming winter season. For a particular coat, his cost per coat is $150 and the retail selling price is $210. He estimates an average sales of 100 coats but with considerable uncertainty, which he express as uniform distribution between 75 and 125. Any coat not sold at the end of the season can be disposed of at cost of $100 to a discount house. Also, Derimod feels that on any such coat he has lost money because of the capital tied up in the inventory for the whole season. He estimates a loss of $15 for every coat that must be sold at the end of the season.

a) What is the cost of underage and cost of overage?

b) How many coats should he order? (For uniform distribution F(x)=(x-a)/(b-a) for axb)

c) Ali manages to learn about new tax levels before his buying decision. This changes his probability distribution to a normal form with a mean of 110 and a standard deviation of 15. Now, what is the best order quantity?

d) Although the average demand considered in part b part c are the same, the optimal quantities are different. Why?