A retail chain is considering placing its last order for a refrigerator model that is going to be phased out and replaced by a new model by the manufacturer. The retail chain sells the refrigerator for $450 and pays a wholesale price of $275 to the manufacturer. Each refrigerator that is not sold by the retail chain before the new model is introduced will be sold to an appliance discount store for $175 each. The manufacturer's fixed production cost is $120,000 and variable production cost is $100. Neither the retailer nor the manufacturer has any inventory of the refrigerator. Following is the demand distribution that the retail chain faces during the selling season for the old model (that is before the new model is introduced.)

9 Demand (units) Probability 500 0.10 1000 0.20 1500 0.35 2000 0.15 2500 0.10 3000 0.10 a. Assume that there are no supply contracts and retail chain wants to maximize its expected profits. How many units should the retailer order and at this order level what will be the retailer's expected profit and what will be the manufacturer's profit? b. What is the highest expected profit the supply chain can hope to achieve? Please note that 3,000 is the maximum demand. Therefore no more than 3000 units can be sold. c. Design a supply contract to more equitably distribute the highest profit between the supplier and the retailer. The supply contract you design should be either a buy-