PA 13-4 Fashionables is a franchisee of The Unlimited, the... 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 500 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 Unlimited offers the sweaters to Fashionables at the wholesale price of $42 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 $16 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. 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 Say Fashionables orders 725 of each sweater. What is Fashionables' expected profit? Use Table 13.4. d Say Fashionables orders 725 of each sweater. What is the stockout probability for each sweater? Use Excel. (Round your answer to 4 decimal places.) TABLE 13.4 The Distribution, FQ), and Expected Inventory, I(), Functions for the Standard Normal Distribution Function - z Iz 7 455 -1.3 0/ 96 .115 FzQg) .91921.4367 93321.523 12 .056 1 1.6 1357 06B6 .94521.5232 -1.0 .1597 0933 17 .9554 17183 -0.9 .184 1 .1004 .95411.3 143 0. .1202 .7131.91 11 21 1 ,2420 1429 2.0 97722.00B5 -0,7 -0.6 -0.5 3743 167 .3085 .197g .982 2,7065 .98612.2049 .93932.3037 99 1 2 .4027 -3. -0. 3446 .2304 NNNNN 3821 2568 Fa =40 .000/0 .0000 -3.9 .0000 0000 -3. OOO1 OOOO -3.7 .0001 OOO0 -3.6 .0002 .0000 -35 .0002 .0001 -3.4 .0003 0001 -3.3 ,0005 OO07 -3.2 .OO07 _OO02 .00100 003 -30 .0013 .0004 -2.9 .0019 0005 -2. ,0026 OOOB -27 O035 OO -2.6 .0047 .0015 .0062 .0020 -2.4 ,00B2 ,0027 =23 ,07 07 100037 0139 OC49 -2.1 .0179 OO65 .022 .0035 -1. g 02370 =.g ,0359 0 43 -1704 46093 -0.3 -0.2 .4 207 3069 9932.5020 460 359 0 5OOO 39B9 .99532.6015 .99652.7011 .99742.300g 539g .4509 | S =2 5793 5069 99g 2.g/O05 3.0 -22 .6 17g 5668 ,6554 46304 .69 15 46973 7257 .7687 75034 29 7B 202 .99a73 .0OMU4 .99903, 003 .99933.2002 .99953.3001 .9973.4001 .9993.5007 .9993 ,6OCOO 3,6 3.7 -1.6 -15 - 1.4 .054g 0 65 .0B0 0 232 .0293 .0367 1.0 1.1 1. 2 1.3 B1591,0OC4 .B4 131.0B33 .B6431.16B6 884g1.256 .90321,3455 3. 3. 9 4. 0 .99993.7OOG 99993.BOO0 1.OOO03.9OO0 1.OOO04 .0000 PA 13-4 Fashionables is a franchisee of The Unlimited, the... 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 500 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 Unlimited offers the sweaters to Fashionables at the wholesale price of $42 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 $16 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. 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 Say Fashionables orders 725 of each sweater. What is Fashionables' expected profit? Use Table 13.4. d Say Fashionables orders 725 of each sweater. What is the stockout probability for each sweater? Use Excel. (Round your answer to 4 decimal places.) TABLE 13.4 The Distribution, FQ), and Expected Inventory, I(), Functions for the Standard Normal Distribution Function - z Iz 7 455 -1.3 0/ 96 .115 FzQg) .91921.4367 93321.523 12 .056 1 1.6 1357 06B6 .94521.5232 -1.0 .1597 0933 17 .9554 17183 -0.9 .184 1 .1004 .95411.3 143 0. .1202 .7131.91 11 21 1 ,2420 1429 2.0 97722.00B5 -0,7 -0.6 -0.5 3743 167 .3085 .197g .982 2,7065 .98612.2049 .93932.3037 99 1 2 .4027 -3. -0. 3446 .2304 NNNNN 3821 2568 Fa =40 .000/0 .0000 -3.9 .0000 0000 -3. OOO1 OOOO -3.7 .0001 OOO0 -3.6 .0002 .0000 -35 .0002 .0001 -3.4 .0003 0001 -3.3 ,0005 OO07 -3.2 .OO07 _OO02 .00100 003 -30 .0013 .0004 -2.9 .0019 0005 -2. ,0026 OOOB -27 O035 OO -2.6 .0047 .0015 .0062 .0020 -2.4 ,00B2 ,0027 =23 ,07 07 100037 0139 OC49 -2.1 .0179 OO65 .022 .0035 -1. g 02370 =.g ,0359 0 43 -1704 46093 -0.3 -0.2 .4 207 3069 9932.5020 460 359 0 5OOO 39B9 .99532.6015 .99652.7011 .99742.300g 539g .4509 | S =2 5793 5069 99g 2.g/O05 3.0 -22 .6 17g 5668 ,6554 46304 .69 15 46973 7257 .7687 75034 29 7B 202 .99a73 .0OMU4 .99903, 003 .99933.2002 .99953.3001 .9973.4001 .9993.5007 .9993 ,6OCOO 3,6 3.7 -1.6 -15 - 1.4 .054g 0 65 .0B0 0 232 .0293 .0367 1.0 1.1 1. 2 1.3 B1591,0OC4 .B4 131.0B33 .B6431.16B6 884g1.256 .90321,3455 3. 3. 9 4. 0 .99993.7OOG 99993.BOO0 1.OOO03.9OO0 1.OOO04 .0000