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 optimalproductionquantityandexpectedprofitunderglobal 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