. Consider the following demand scenario:

Quantity	Probability
2,000	0.03
2,100	0.08
2,200	0.15
2,300	0.30
2,400	0.17
2,500	0.12
2,600	0.10
2,700	0.05

Suppose the manufacturer is make-to-stock; that is the timing of events is as follows:

• The manufacturer produces a certain amount
• The distributor receives firm orders from the retailer
• The distributor orders from the manufacturer.

The manufacturer produces at a cost of $20/unit, sells to the distributor for $40/unit and the distributor sells to end customer (retailer) for $60/unit. Unsold units are sold for $10 after the season.

1. What is the optimal production level for the manufacturer? What is the expected profit for the manufacturer and distributor?
2. What is the optimal production level for the manufacturer if the distributor agrees to pay 12% of the manufacturers cost? What will be the expected profit for the manufacturer and for the distributor in this cost sharing arrangement? Do both parties benefit from this agreement?
3. What is the Optimal production level for the manufacturer if the distributer agrees to pay 25% of the manufacturers cost in exchange for the manufacturer to reduce his wholesale price to $34? What will be the expected profit for the manufacturer and for the distributor in this cost sharing arrangement? Compared to the situation in part (a) above, do both parties benefit from this agreement?