Please show your work including excel formulas you used. Explain each step throughly.

Q14.5 (Algo) Fashionables [14.3, 14.4, 14.5] Fashionables is a franchisee of The Limited, the well-known retailer of fashionable clothing. Prior 1o the winter season, The Limited offers Fashionables the choice of five different colors of a particular sweater design. The sweaters are knit overseas by hand, and because of the lead times involved, Fashionables will need 1o order its assortment in advance of the selling season. As per the contracting t2rms offered by The Limited, Fashionables also will not be able 1o cancel, modify, or reorder sweaters during the selling season. Demand for each color during the season is normally distributed with a mean of 720 and a standard deviation of 300. Further, you may assume that the demands for each sweater are independent of those for a different color. The Limited 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 Limited delivers orders placed by Fashionables in truckloads at a cost of $2,000 per truckload. The ransportation cost of $2,000 is borne by Fashionables. Assume unless otherwise specified that all the sweaters ordered by Fashionables will fit into one truckload. Alsc assume that all other associated costs, such as unpacking and handling, are negligible. The Limited 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? (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? (Round your answer to the nearest whole number.)For parts c and d, assume Fashionables orders 920 of each sweater. c. What is Fashionables\" expected profit? (Round your answer to one decimal place.) d. What is the stockout probability for each sweater? (Round your answer to one decimal place.) e. Mow suppose The Limited announces a truckload capacity of 3,600 total units of sweaters. If Fashionables orders more than 3,600 sweaters in total, it will have to pay for two truckloads. What now is Fashionables' optimal order guantity for each type of sweater? (Round your answer to the nearest whole number.)