3. The Apparel Company (ABC) is planning production for its four sweater styles that are popular during Christmas. All four styles have demand that is normally distributed. The best-selling style has an expected demand of 35,000 and a standard deviation of 4,000. Each of the other three styles has an expected demand of 10,000 with a standard deviation of 5,000. 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 of each type should ABC manufacture?

b. What is the expected profit from this policy?

c. How many sweaters does ABC expect to sell at a discount?

d. ABC is considering the postponement of knitting and using flexible machines. This will require the base sweaters to be made in advance (identical for each of the four types) and the final patterns to be knit later. This will increase production cost per sweater to $21.40. How many sweaters should ABC manufacture with postponement? What is the expected profit from this policy?

e. Another option is to produce the popular style without postponement and the other three styles using postponement. What is the expected profit under this policy?