There are two retailers serving the demand in two regional markets separately. Assume the demands in the two regions are independently and identically distributed with probabilities P(Di = 100) = 0.33, P(Di=200) =0.67, i = 1, 2.
(1)  Focus on a single retailer in Questions (1) and (2). Suppose consumers only purchase the product from the store in their region. There is only one selling season for this product, and each retailer orders only once before the selling season starts. The wholesale price is $60, the selling price is $80, and the salvage value for an unsold unit is $20. Please find out the optimal order quantity for each retailer and the retailer’s expected profit.
(2) If the manufacturer lowers the wholesale price to $28, but in return, requests a 30% of revenue sharing from the retailer. Please find out the optimal order quantity for each retailer.
(3) Forget the revenue sharing contract in Question (2), and use the prices in Question (1) for the remaining questions. Find out the scenarios of the total demand in the two regions. (Hint: Remember the example about red and black T-shirts?)
(4) Now suppose if either store is out of stock, then 70% of its unsatisfied customers will go to the store in the other region, if stock is available there. If Retailer 1 orders 100 units and Retailer 2 orders 200 units, what is Retailer 2’s expected sales and expected profit?