A manufacturing supplier produces faux fur coats in a large North American city. In the spring of each year, she must decide on the number of each type of fur coat to produce for the upcoming winter season. For a particular line, her cost per coat is $150 and the selling price is $200. She estimates an average sale of 100 coats but with considerable uncertainty, which she is willing to express as a normal distribution with a variance 200. Any coat not sold at the end of the winter can be disposed of to a discount house. However, she feels that on any such coat she has lost money because of the capital tied up in the inventory for the whole season. She estimates a loss of $0.15 for every dollar tied up in a coat that must be sold off at the end of the season.

a. How many coats should she produce?

b. What is the expected understock?

c. What is the expected overstock?

d. What is the expected profit?