Question

I need help with C. I got wrong answers.It is not 7050 or 1218. I need tp use 13.4 table.

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. 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 distnbuted with a mean of 575 and a standard deviation of 225 Further, you may assume that the demand for each sweater is independent of the demand for any other color The sweaters are knit overseas by hand, and because of the lead times involved, Fashionables will The UnLimited offers the sweaters to Fashionables at the wholesale price of $44 per sweater, and Fashionables plans to sell each sweater at the retail price of $65 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 $15 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 How many units of each sweater-type should Fashionables order to maximize its expected profit? Use Table 13.4 and round to nearest integer 530 If Fashionables wishes to ensure a 97.5% in-stock probability, what should its order quantity be for each type of sweater? Use Table 13.4 and round to nearest integer b. 1,025 Say Fashionables orders 650 of each sweater. What is Fashionables' expected profit? Use Table 13.4 1,218 C. 0.3694 d. (Round your answer to 4 decimal places) TABLE 13.4 The Distribution, FiO), and Expected Inventory. NO). Functions for the Standard Normal Distribution Function Fn) -4.0 3.9 -3.8 3.7 -3.6 3.5 3.4 3.3 3.2 0968 0455 0561 0686 0833 1004 9192 9332 9452 14367 1.5293 1.6232 7183 8143 19111 20085 2.1065 2.2049 2.3037 0001 0001 0002 0002 0003 0001 -08 9713 0001 2420 743 085 429 1687 1978 2304 9821 9861 9893 9918 9938 9953 9965 9974 9981 9987 0007 0010 0013 0019 0026 0035 0047 0002 2.2 -0.4 3821 24027 0005 0008 0011 0015 0020 0027 0037 0049 4207 3069 2.8 3509 2 6015 2.7011 2.8008 2.9005 3.0004 3.1003 3.2002 3.3001 3.4001 3.5001 3.6000 3.7000 3.8000 3.9000 5398 5793 6179 6554 509 2.8 2.5 2 5069 0082 0107 0139 0179 -2.3 -2.2 -2.1 6304 6978 7687 8429 9202 10004 1.0833 1.1686 1.2561 9993 7257 0085 0111 0143 997 0287 7881 8159 8413 8643 8849 90321.345 3.5 3.6 0446 0548 0668 0808 0232 0293 0367 3.8 1.0000 4.0 1.0000

Answer 1

Cs = Cost of underage = selling price -cost = 65-44 =21

Co =Cost of excess = cost - salvage value = 44-15 =29

Service level = Cs / Cs+Co = 21/19+21 = 21/50 =0.42

which corresponds to the z value of -0.2

(a) Number of sweaters to be ordered

= mean + SD x z value

= 575 + 225x(-0.2) = 575-45 =530

(b) Order value for 97.5% in stock probability

z value for above service level is 1.96

Order quantity = 575 + 1.96x225 = 1016

(d) If 650 sweaters are ordered, the z value

650 = 575 + z x225

z = 75/225 =0.333

which corresponds to a in service probability of 0.6293

Probabiltity of stock out = 1-0.6293 =0.3707

(c) service level with 650 sweaters = 0.63

lost sales factor at z =0.63

L(0.63) = 0.16

Expected lost sales = L(z)x sigma = 0.16 x225 =36

Expected sales = mean - expected lost sales = 575 -36 =539

Expected leftover inventory = Quantity -expected sales = 650-539 =111

Expected profit = Cs xExpected sales - Co x expected leftover inventory

= 21x539 - 29 x111 = 11319 -3219 = 8100