TABLE 13.4 The Distribution, F(Q), and Expected Inventory, I(Q), Functions for the Standard Normal Distribution Function z F(z) 1(z) - -4.0 .0000 .0000 -3.9 .0000 .0000 -3.8 .0001 .0000 -3.7 .0001 .0000 -3.6 .0002 .0000 -3.5 .0002 .0001 -3.4 .0003 .0001 -3.3 .0005 .0001 -3.2 .0007 .0002 -3.1 .0010 .0003 -3.0 .0013 .0004 -2.9 .0019 .0005 -2.8 .0026 .0008 -2.7 .0035 .0011 -2.6 .0047 .0015 -2.5 .0062 .0020 -2.4 .0082 .0027 -2.3 .0107 .0037 -2.2 .0139 .0049 -2.1 .0179 .0065 -2.0 .0228 .0085 -1.9 .0287 .0111 -1.8 .0359 .0143 -1.7 .0446 .0183 -1.6 .0548 0232 -1.5 10668 10293 -1.4 10808 10367 -13 0968 10455 -12 1151 0561 -1.1 1357 10686 -1.0 1587 10833 -09 11841 1004 -0.8 2119 1202 -0.7 12420 1429 -0.6 2743 1687 -0.5 13085 1978 -0.4 13446 12304 -03 3821 12668 -0.2 4207 3069 -0.1 4602 3509 5000 13989 5398 4509 5793 15069 .6179 15668 16554 16304 16915 16978 7257 7687 17580 18429 7881 19202 18159 1.0004 10 1843 1.0833 18643 1.1686 18849 12561 19032 1.3455 1.4 9192 1.4367 1.5 19332 1.5293 19452 1.6232 19554 17183 19641 1.8143 19 19713 1.911 2.0 19772 2.0085 19821 2.1065 v - 2.2 19861 2.2049 23 19893 2.3037 2.4 1998 2.4027 2.5 19938 2.5020 2.6 19953 2.6015 19965 2.7011 2.8 19974 2.8008 2.9 19981 29005 3.0 19987 3.0004 19990 3.1003 3.2 19993 3.2002 3.3 19995 3.3001 3.4 19997 3.4001 3.5 19998 3.5001 19998 3.6000 36 3.7 19999 3.7000 3.8 19999 3.8000 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; 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 425 and a standard deviation of 150. Further, you may assume that the demands for each sweater are independent of those for a different color. Use Table 13.4 The Unlimited offers the sweaters to Fashionables at the wholesale price of $43 per sweater, and Fashionables plans to sell each sweater at the retail price of $74 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 $24 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. If Fashionables wishes to ensure a 97.5 percent in-stock probability, what should its order quantity be for each type of sweater? Use Table 13.4. Say Fashionables orders 700 of each sweater. What is Fashionables' expected profit? Use Table 13.4. Say Fashionables orders 700 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, F(Q), and Expected Inventory, I(Q), Functions for the Standard Normal Distribution Function z F(z) 1(z) - -4.0 .0000 .0000 -3.9 .0000 .0000 -3.8 .0001 .0000 -3.7 .0001 .0000 -3.6 .0002 .0000 -3.5 .0002 .0001 -3.4 .0003 .0001 -3.3 .0005 .0001 -3.2 .0007 .0002 -3.1 .0010 .0003 -3.0 .0013 .0004 -2.9 .0019 .0005 -2.8 .0026 .0008 -2.7 .0035 .0011 -2.6 .0047 .0015 -2.5 .0062 .0020 -2.4 .0082 .0027 -2.3 .0107 .0037 -2.2 .0139 .0049 -2.1 .0179 .0065 -2.0 .0228 .0085 -1.9 .0287 .0111 -1.8 .0359 .0143 -1.7 .0446 .0183 -1.6 .0548 0232 -1.5 10668 10293 -1.4 10808 10367 -13 0968 10455 -12 1151 0561 -1.1 1357 10686 -1.0 1587 10833 -09 11841 1004 -0.8 2119 1202 -0.7 12420 1429 -0.6 2743 1687 -0.5 13085 1978 -0.4 13446 12304 -03 3821 12668 -0.2 4207 3069 -0.1 4602 3509 5000 13989 5398 4509 5793 15069 .6179 15668 16554 16304 16915 16978 7257 7687 17580 18429 7881 19202 18159 1.0004 10 1843 1.0833 18643 1.1686 18849 12561 19032 1.3455 1.4 9192 1.4367 1.5 19332 1.5293 19452 1.6232 19554 17183 19641 1.8143 19 19713 1.911 2.0 19772 2.0085 19821 2.1065 v - 2.2 19861 2.2049 23 19893 2.3037 2.4 1998 2.4027 2.5 19938 2.5020 2.6 19953 2.6015 19965 2.7011 2.8 19974 2.8008 2.9 19981 29005 3.0 19987 3.0004 19990 3.1003 3.2 19993 3.2002 3.3 19995 3.3001 3.4 19997 3.4001 3.5 19998 3.5001 19998 3.6000 36 3.7 19999 3.7000 3.8 19999 3.8000 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; 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 425 and a standard deviation of 150. Further, you may assume that the demands for each sweater are independent of those for a different color. Use Table 13.4 The Unlimited offers the sweaters to Fashionables at the wholesale price of $43 per sweater, and Fashionables plans to sell each sweater at the retail price of $74 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 $24 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. If Fashionables wishes to ensure a 97.5 percent in-stock probability, what should its order quantity be for each type of sweater? Use Table 13.4. Say Fashionables orders 700 of each sweater. What is Fashionables' expected profit? Use Table 13.4. Say Fashionables orders 700 of each sweater. What is the stockout probability for each sweater? Use Excel. (Round your answer to 4 decimal places.)