Use Table 13.4 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, and 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 demand for each sweater is independent of the demand for any other color. 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 for a 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 and round to nearest integer. 575 If Fashionables wishes to ensure a 97.5% in-stock probability, what should its b. order quantity be for each type of sweater? Use Table 13.4 and round to nearest integer. 900 C. Say Fashionables orders 750 of each sweater. What is Fashionables' expected profit? Use Table 13.4. ********* TABLE 13.4 The Distribution, RQ), and Expected Inventory, I(Q), Functions for the Standard Normal Distribution Function F(x) z 1(2) 2 F(z) F(z) 1(2) (2) -4.0 0000 0000 -1.3 0968 .9192 0455 14 1.4367 -3.9 0000 0000 -1.2, 1151 0561 1.5 9332 1.5293 -3.8 0001 0000 1357 .0686 1.6 9452 1.6232 -3.7 0001 0000 -1.0 1587 0833 1.7 9554 1.7183 -3.6 0002 0000 -0.9 1841) 1004 1.8 9641 1.8143 -3.5 0002 0001 -0.8 21191 1202 1.9 1.9111 9713 -3.4 0003 0001 -0.7 2420 1429 2.0 9772 2.0085 -3.3 0005 0001 -0.6 2743 1687 2.1 9821 2.1065 -3.2 0007 0002 -0.5 3085 1978 2.2 9861 2.2049 -3.1 0010 0003 -0.4 3446 2304 2.3 9893 2.3037 -3.0 0013 0004 -0.3 3821 2668 2.4 .9918 2.4027 -2.9 0019 0005 -0.2 4207 3069 2.5 9938 2.5020 -2.8 0026 .0008 -0.1 4602 3509 2.6 9953 2.6015 -2.7 0035 0011 .0 .5000 3989 2.7 9965 2.7011 -2.6 0047 0015 5398 4509 9974 2.8008 -2.5 0062 0020 .5793 5069 9981 2.9005 -2.4 0082 0027 6179 5668 9987 3.0004 -2.3 0107 0037 .6554 .6304 9990 3.1003 -2.2 0139 0049 6915 6978 9993 3.2002 -2.1 0179 0065 7257 .7687 9995 3,3001 -2.0 0228 0085 7580 8429 9997 3.4001 -1.9 0287 0111 7881 9202 9998 3.5001 -1.8 0359 0143 8159 1.0004 9998 3.6000 -1.7 0446 0183 8413 1.0833 9999 3.7000 -1.6 0548 0232 .8643 1.1686 9999 3.8000 -1.5 0668 0293 8849 1.2561 1,0000 3.9000 -1.4 0808 0367 .9032 1.3455 1.0000 4.0000 .1 2 3 A 5 6 7 .8 .9 1.0 1.1 1.2 1.3 2.8 2.9 3.0 3.1 3.2 3.3 3,4 3.5 3.6 3.7 3.8 3.9 4.0