Question

Fashionables is a franchisee of The UnLimited, the wel-known retailer of fashionable clothing Prior to the winter season. The UnLimited offers Fashionables the choice of five Use Jable 13.4 diferent colors of a particular sweater design. The swoaters are knt overseas by hand, and because of the lead tmes involved, Fashionables will need to order its assortment in advance of the seling season. As per the contracting terms oflered by The UnLimited, Fashionables will also not be able to cancel, modty or reorder sweaters during the seling season Demand for each color during the season is normaly distr with a mean of S00 and a standard devat on 이 200 Further, you may assume that the demand for each sweater independent of the demand for any other color The UnLmited offers the sweaters to Fashionables at the wholesale price of $40 per sweater, and Fashionables plans to sell each sweater at the retal price of $70 per unit. The UnLimited does not accept any returns of unsold inventory However, Fashionables can sel al of the unsold sweaters at the end of the season at the fire-sale price of $20 each It a part of the question specifies whether to use Table 13.4, or to use Excel, then credt for a correct answer will depend on using the specfied method How mamy unts ol each sweater ype shouid Fashionables order to maxmize its expected proft? Use Table 13.4 b. If Fash orables wstes lo ensurea 97.5% in-stock probablity, what should its order quaraty be for each type of sweater? Use Table 13.4 e. Say Fashionabikes culers 725 of each sweater. Whet is Fashlonablen exsced proti? Use Table 13.4 d. Say Fashionables orders 725 of each swealer. What is the stockout probabilty for each sweater? Use Excel Round your answer to 4 decimal places TABLE 13.4 The Distribution. FiO), and Expected Inventory, O), Functions for the Standard Normal Distribution Function I(a) 0455 9192 9332 9452 9554 1357 1587 1841 2119 2420 2743 3085 3446 3821 4207 4602 1.4367 1.5293 1.6232 1.7183 1.8143 19111 2.0085 2.1065 2.2049 2.3037 2.4027 2.5020 9953 2.6015 2.7011 28008 2.9005 3.8 0686 0833 0002 1202 1429 1687 1978 2304 2668 3069 3509 3989 4509 5069 5668 6304 6978 7687 8429 9202 9713 9772 9821 9861 0003 0007 0010 0013 0019 0026 0035 0047 0062 0082 0107 0139 0179 0228 0287 0359 0446 0548 0668 0002 -0.5 0003 9918 9938 2.8 0008 2.6 0011 9965 5398 5793 6179 6554 6915 9974 0020 0027 0037 0049 3.0 9987 9990 9993 9995 3.1003 3.2002 3.3001 3.4001 3.5001 0085 .7 7580 7881 9998 0143 0183 0232 0293 0367 1.8 1.0833 1.1686 1.2561 1.3455 8643 8849 9032 3.7 3.8 3.7000 3.8000 3.9000 1.0000

Answer 1

Fashionables, a franchise of the UnLimited Mean demand, μ Standard deviation of demand, σ Retail Selling price, SP Wholesale price, CP Salvage value, SV 500 200 $ 70 40 $ 20 Underage penalty, Cu 70 40 Overage penalty, Co 40 20 30 Selling price - Cost price 20 Cost price - Salvage value 0.6 ECu/ (Co Cu)- Critical ratio, F[z) Standard Normal Variate, z lookup value of z in table 13.4 for F(z)>-0.6 0 500 a) Optimal Order Quantity, Q -μ +z*σ Target in-stock, F(z 97.5% 2 900 Standard Normal Variate, z lookup value of z in table 13.4 for F(z)>-0.975 b) Optimal Order Quantity, Q -μ +z*σ Given order quantity, Q Standard Normal Variate, z l(z) Expected inventory, V Expected Sales, S 725 1.125 1.1903 238.06 486.94 9847 49235 F(Q-H)/a lookup value of I(z) in table 13.4 for z-1.125 - -σ*1(2) EQ-V Expected profit for each sweater-type ES*Cu V*Co c) Expected profit for all 5 sweater-tvpe 9847*5 Standard Normal Variate, z 1.1250 :(Q-H/O :1-NORMSDIST(z) d) Stockout probabilit 0.1303 =