Fashionables is a franchisee of The UnLimited, the well-known retailer of fashionable clothing. Prior to the winter season, 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 400 and a standard deviation of 250. Further, you may assume that the demands for each sweater are independent of those for a different color. Use Table 13.4

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The UnLimited offers the sweaters to Fashionables at the wholesale price of $36 per sweater, and Fashionables plans to sell each sweater at the retail price of $66 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 $25 each.

If a part of the question specifies whether to use Table 13.4, or to use Excel, then credit f correct answer will depend on using the specified method.

a. How many units of each sweater type should Fashionables order to maximize its expected profit? Use Table 13.4. (Round your answer to the nearest whole number.)

b. If Fashionables wishes to ensure a 97.5 percent in-stock probability, what should its order quantity be for each type of sweater? Use Table 13.4. (Round your answer to the nearest whole number.)

c. Say Fashionables orders 750 of each sweater. What is Fashionables' expected profit for all five sweater colors? Use Table 13.4. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

d. Say Fashionables orders 750 of each sweater. What is the stockout probability for each sweater? Use Excel. (Round your answer to 4 decimal places.)