Benetton has entered into a quantity flexibility contract with a retailer for a seasonal product. If the retailer orders O units, Benetton is willing to provide up to another 35 percent if needed. Benetton’s production cost is $20, and it charges the retailer a wholesale price of $36. The retailer prices to customers at $55 per unit. Any unsold units can be sold by the retailer at a salvage value of $25. Benetton can salvage only $10 per unit for its leftover inventory. The retailer forecasts demand to be normally distributed, with a mean of 4,000 and a standard deviation of 1,600.
a. How many units O should the retailer order?
b. What is the expected quantity purchased by the retailer (recall that the retailer can increase the order by up to 35 percent after observing demand)?
c. What is the expected quantity sold by the retailer?
d. What is the expected overstock at the retailer?
e. What is the expected profit for the retailer?
f. What is the expected profit for Benetton?