The Knitting Company (TKC) is planning production for its sweaters that are popular during Christmas. The demand is normally distributed with an expected demand of 8,000 with a standard deviation of 4,000. Currently all sweaters are produced before the start of the season. Production cost is $ 20 per sweater, and they are sold for a wholesale price of $ 35. Any unsold sweaters at the end of the season are discounted to $ 15, and they all sell at that price. It costs $ 2 to hold the sweater in inventory for the entire season if it does not sell.
a. How many sweaters should TKC manufacture?
b. What is the expected profit from this policy?
c. How many sweaters does TKC expect to sell at a discount?