Consider the following demand scenario:

Quantity 2100 2200 2300 2400 2500 2600

Probability 10% 16% 30% 17% 12% 15%

Suppose the manufacturer produces at a cost of $20/unit, and sells to the distributor at $40/unit. The distributor sells to end customers for $50/unit during season. The unsold units are sold for $4/unit after season. The timing of events is as follows:

• The manufacturer produces a certain amount.
• The distributor observes demand.
• The distributor orders from the manufacturer.
• Questions:

(1) What is the expected profit for the manufacturer and distributor?

(2) Find a pay-back contract such that both the manufacturer and distributor enjoy a higher

profit than (1), and calculate their expected profits.