4. Fashionables is a franchisee of The UnLimited, the well-known retailer of fashionable clothing. Prior to the winter season, Page 442 The UnLimited offers Fashionables the choice of five different colors of a particular sweater design. The sweaters are knit overseas by hand; because of the lead times involved, Fashionables will need to order its assortment in advance of the selling season. As per the contracting terms offered by The UnLimited, Fashionables will also not be able to cancel, modify, or reorder sweaters during the selling season. Demand for each color during the season is normally distributed with a mean of 500 and a standard deviation of 200. Further, you may assume that the demands for each sweater are independent of those for a different color. The UnLimited offers the sweaters to Fashionables at the wholesale price of $40 per sweater, and Fashionables plans to sell each sweater at the retail price of $70 per unit. The UnLimited does not accept any returns of unsold inventory. However, Fashionables can sell all of the unsold sweaters at the end of the season at the fire-sale price of $20 each. a. How many units of each sweater type should Fashionables order to maximize its expected profit? b. If Fashionables wishes to ensure a 97.5 percent in-stock probability, what should its order quantity be for each type of sweater? c. Say Fashionables orders 725 of each sweater. What is Fashionables' expected profit? d. Say Fashionables orders 725 of each sweater. What is the stockout probability for each sweater