1. (9 pts) Consider a supply chain with a manufacturer and a retailer. The product is offered for a single season. Suppose the manufacturer produces at a cost of $30/unit. The manufacturer sells to the retailer at $40/unit. The retailer sells to end customers for $50/unit during season and unsold units are sold for $10/unit salvage value after season. The demand scenario is given by the following table: Quantity 3000 4000 5000 6000 a. Probability 26% 15% 30% 29% (3 pts) What is the global optimal production quantity that maximizes the total profit for both firms? Give this production quantity, what are the retailer's expected profit and manufacturer's profit? b. (3 pts) If the retailer is self-interested, how much should the retailer order? Give this order quantity, what are the retailer's expected profit and the manufacturer's expected profit? c. (3 pts) Suppose the manufacturer offers a buy-back contract at price b=$30. How much would the retailer order now? What are the retailer's and the manufacturer's expected profits?