-Consider two companies involved in the supply chain: a retailer who faces customer demand and a manufacturer who produces and sells ski jackets to the retailer

-Consider two companies involved in the supply chain: a retailer who faces customer demand and a manufacturer who produces and sells ski jackets to the retailer. It costs the manufacturer $30 to manufacture and ship each ski jacket. The retailer plans to sell the ski jacket for $300. At this price, demand for the ski jackets is estimated to be 10000 units with a 20 percent chance of happening, 9000 units with a 40 percent chance of happening, and 8000 units with a 40 percent chance of happening. Any ski jacket not sold during the ski season is sold to a discount store for $20. We refer to this value as the salvage value. Both the manufacturer and the retailer can sell the ski jackets they still have on hand after season for this salvage value.
-(a)Suppose the manufacturer sells to the retailer at $80/unit. How many ski jackets should the retailer order? How much profit does the retailer expect to make as a result? How much profit will the manufacturer make as a result?
-(b)What is the system optimal production quantity and expected profit under global optimization?
-(c) Is it possible to find a contract such that both the manufacturer and retailer enjoy a higher expected profit than a)? If so, describe the contract and calculate the expected profit for the manufacturer and the retailer. If not, explain why it is not possible.