Benetton has 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 the 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?