Consider a retailer that sells summer fashion items such as swimsuits. About 6 months before summer, the retailer must place an order to the manufacturer for all its products. Since there is no clear indication of how the market will respond to the new designs, the retailer needs to use various tools to predict demand for each design, and decide order quantity accordingly.

To assist management in these decisions, the marketing department uses historical data from the last 5 years, current economic conditions, and other factors to construct a probabilistic forecast of the demand for swimsuits. They have identified several possible scenarios for sales in the coming season, based on such factors as possible weather patterns and competitors behavior, and assigned each a probability of occurring (see the following Table). For example, the marketing department believes that a scenario that leads to 8,000 unit sales has an 11 percent chance of happening. We have the following additional information:

- The manufacturer produces the quantities that the retailer orders. - The production cost per unit equals $40. - During the summer season, the selling price of a swimsuit is $120 per unit. - The wholesale price paid by the retailer to the manufacturer is $60 per unit. - Any swimsuit not sold during the summer season is sold to a discount store for $20. We refer to this value as the salvage value

Demand Probability 8,000 11% 10,000 11% 12,000 28% 14,000 22% 16,000 18% 18,000 10% a) How much should the retailer order from the manufacturer?

b) Suppose the retailer and the manufacturer belong to the same company. The company designs, produces and sells swimsuits. How much should the company produce? Did you get a different answer than the order quantity in a)? Why is there a difference?

c) Back to the original setting where the retailer and the manufacturer are two entities. If the retailer and the manufacturer decide to adopt a buyback contract. In this contract, the seller agrees to buy back unsold goods from the buyer for $b per unit. Given the wholesale price (i.e., $60), what is the optimal buyback price?