(a) Suppose the manufacturer sells to the retailer at $80/unit. How many ski jackets should the retailer order? How much profit does the retailer expect to make as a result? How much profit will the manufacturer make as a result?

(b) What is the system optimal production quantity and expected profit under global optimization?

(c) Is it possible to find a contract such that both the manufacturer and retailer enjoy a higher expected profit than a)? If so, describe the contract and calculate the expected profit for the manufacturer and the retailer. If not, explain why it is not possible.