Benetton is planning production for four sweater styles that are popular during I. Christmas. All four...

 

Transcribed Image Text:

Benetton is planning production for four sweater styles that are popular during I. Christmas. All four styles have demand that is normally distributed. The bestselling style has an expected demand of 40,000 and a standard deviation of 6,000. Each of the other three styles has an expected demand of 9,000 with a standard deviation of 4,000. Currently all sweaters are produced before the start of the season-that is, a make-to- stock environment. Production cost is $21 per sweater and they are sold for a wholesale price of $38. Any unsold sweaters at the end of the season are discounted to $16 and they all sell at that price. However, it costs $3 to hold the sweater in inventory for the entire season up until the time it sells at a discount. (note: these prices and costs are the same for each sweater). a. What is the cost of being understocked for each sweater? b. What is the cost of being overstocked for each sweater? Cost Price - Salvage c. What is the in-stock probability that Benetton should target to maximize the expected profit from each sweater? d. How many sweaters of each type should Benetton produce to maximize its expected profit? e. What is the expected profit for each sweater and the total expected profit for all sweaters? f. For the expected profit maximizing quantity, Q*, how many sweaters of each type are expected to be sold at a discount? Benetton is planning production for four sweater styles that are popular during I. Christmas. All four styles have demand that is normally distributed. The bestselling style has an expected demand of 40,000 and a standard deviation of 6,000. Each of the other three styles has an expected demand of 9,000 with a standard deviation of 4,000. Currently all sweaters are produced before the start of the season-that is, a make-to- stock environment. Production cost is $21 per sweater and they are sold for a wholesale price of $38. Any unsold sweaters at the end of the season are discounted to $16 and they all sell at that price. However, it costs $3 to hold the sweater in inventory for the entire season up until the time it sells at a discount. (note: these prices and costs are the same for each sweater). a. What is the cost of being understocked for each sweater? b. What is the cost of being overstocked for each sweater? Cost Price - Salvage c. What is the in-stock probability that Benetton should target to maximize the expected profit from each sweater? d. How many sweaters of each type should Benetton produce to maximize its expected profit? e. What is the expected profit for each sweater and the total expected profit for all sweaters? f. For the expected profit maximizing quantity, Q*, how many sweaters of each type are expected to be sold at a discount?