To ensure a full line of outdoor clothing and accessories, the marketing department at Teddy Bower insists that they also sell waterproof hunting boots. Unfortunately, Teddy Bower does not have expertise in manufacturing those kinds of boots. Hence, Teddy Bower contacted several Taiwanese suppliers to request quotes. Due to competition, Teddy Bower knows that it cannot sell these boots for more than $54. However, $49 per boot was the best quote from the suppliers. In addition, Teddy Bower anticipates excess inventory will need to be sold off at a 50% discount at the end of the season. Given the $54 price, Teddy Bower's demand forecast is 400 boots, with a standard deviation of 300.

1. If Teddy Bower decides to include these boots in its assortment, how many boots should Teddy Bower order from the supplier? Use Table 13.4
2. Suppose Teddy Bower orders 380 boots. What is Teddy Bower's expected profit (round to the nearest integer)? Use Table 13.4.
3. The marketing department insists that their in-stock probability be at least 98%. Given this mandate, how many boots do they need to order? Use Table 13.4.

TABLE 13.4 The Distribution, F(Q), and Expected Inventory, /(Q), Functions for a Normal Distribution with Mean 3000 and Standard Deviation 1000 F(z) 1(z) F(z) (z) F(z) -4.0 0000 0000 -1.3 0968 .0455 1.4 9192 1.4367 -3.9 .0000 0000 -1.2 1151 .0561 1.5 9332 1.5293 -3.8 0001 0000 -1.1 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 .2119 1202 1.9 .9713 1.9111 -3.4 0003 0001 0.7 2420 .1429 2.0 9772 2.0085 -3.3 .0005 0001 0.6 .2743 1687 2.1 .982 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 .1 5398 4509 2.8 .9974 2.8008 -2.5 0062 0020 .2 5793 .5069 2.9 9981 2.9005 -2.4 0082 .0027 .3 6179 .5668 3.0 9987 3.0004 -2.3 0107 0037 .4 6554 6304 3.1 9990 3.1003 -2.2 0139 .0049 .5 6915 6978 3.2 9993 3.2002 -2.1 0179 .0065 .6 7257 7687 3.3 .9995 3.3001 -2.0 0228 0085 .7 7580 8429 3.4 .9997 3.4001 -1.9 0287 0111 .8 .7881 9202 3.5 9998 3.5001 -1.8 0359 .0143 9 8159 1.0004 3.6 9998 3.6000 -1.7 0446 .0183 1.0 .8413 1.0833 3.7 9999 3.7000 -1.6 0548 0232 1.1 .8643 1.1686 3.8 9999 3.8000 -1.5 0668 .0293 1.2 8849 1.2561 3.9 1.0000 3.9000 -1.4 .0808 0367 1.3 9032 1.3455 4.0 1.0000 4.0000