A company manufactures air conditioners for sale in the U.S. market. An important part in each unit is a compressor obtained from a supplier in Asia. To meet summer demand, the company has to order these compressors in advance. Forecasted demand for the summer is given in Table 1.

Demand	200	300	400	500	600
Probability	5%	15%	30%	30%	20%
F (D)	5%	20%	50%	80%	100%

Table 1: Summer demand for air conditioners

The selling price of an air conditioner is $900. Inventory at the end of the summer season is discarded. Any order not filled from stock is lost (i.e. the customer buys it from the competition). Production costs data are listed in Table 2

Direct labor costs	100$
Variable overhead (per unit)	100$
Direct material costs (other than compressors)	100$
Compressor Wholesale price	300$
Total	600$

Table 2: Cost data

All air conditioners are assembled-to-order (i.e. direct labor costs, variable overhead and direct material costs only occur if a unit is sold). The suppliers costs for producing a compressor are $102.

Questions:

1. The manufacturer and the supplier sign a buyback contract with a buyback price of b. What is the optimal value of b to coordinate the supply chain (i.e. total supply chain profit equals the profit of an integrated company*)?

2. The manufacturer and the supplier sign a revenuesharing contract. The supplier charges the manufacturer its costs, but receives a 25.5%-fraction f_r of the manufacturers revenue. What are the expected profits of the supplier and the manufacturer?

*integrated company: the supplier and the manufacturer belong to the same company group

Please do not forget to interpret all the answers in detail, i.e. to explain and justify! Enter all the intermediate steps in the calculations and specify the units of the results! Pay attention to meaningful rounding!