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Use Table 13.4 CPG Bagels starts the day with a large production run of bagels. Throughout the morning additional bagels are produced as needed. The last bake is completed at 3 pm, and the store closes at 8 pm. It costs approximately $0.20 in materials and labor to make a bagel. The price of a fresh bagel is $0.60. Bagels not sold by the end of the previous day are sold the next day as "day-old" bagels in bags of six, for $0.99 a bag. About two-thirds of the day-old bagels are sold, the remainder are just thrown away. There are many bagel flavors, but for simplicity, concentrate just on the plain bagels. The store manager predicts that demand for plain bagels from 3 pm until closing is normally distributed with mean 60 and standard deviation 23. 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 bagels should the store have at 3 pm to maximize the store's expected profit (from sales between 3 pm until closing)? (Hint: Assume day-old bagels are sold for $0.99/6 = $0.165 each, i.e., don't worry about the fact that day-old bagels are sold in bags of six.) Use Table 13.4 and round-up rule. a. Suppose the store manager has 101 bagels at 3 pm. How many bagels should b. the store manager expect to have at the end of the day? Use Table 13.4 and round-up rule. (Round your answer to a whole number.) Suppose the manager would like to have a 0.91 in-stock probability on demand c. that occurs after 3 pm. How many bagels should the store have at 3 p.m. to ensure that level of service? Use Table 13.4 and round-up rule. TABLE 13.4 The Distribution, F(Q), and Expected Inventory, I(Q), Functions for the Standard Normal Distribution Function -4.0 -3.9 F(z) 0000 .0000 () 0000 0000 z -1.3 -1.2 -1.1 -1.0 -0.9 -0.8 F(z) .0968 1151 1357 1(2) .0455 .0561 .0686 1.4 1.5 1.6 1.7 Hz) 1.4367 1.5293 1.6232 .0000 -3.7 .0000 .0833 -3.6 .1587 .1841 2119 .1004 .0000 .0001 1.8 -3.5 1.9 -0.7 .2420 1202 .1429 1687 .0001 .0001 2.0 1.7183 1.8143 1.9111 2.0085 2.1065 2.2049 2.3037 2.4027 -0.6 2743 2.1 -3.3 -3.2 .0002 .1978 -3.1 .0003 2304 2.3 -0.5 -0.4 -0.3 -0.2 -3.0 2 668 .0004 .0005 .0008 .3069 2.5 2.5020 .0001 .0001 .0002 .0002 .0003 .0005 .0007 .0010 .0013 .0019 .0026 .0035 .0047 .0062 .0082 .0107 .0139 .0179 .0228 .0287 .0359 N -0.1 .3509 2.6 N F(z) 9192 9332 9452 .9554 .9641 9713 .9772 .9821 .9861 .9893 .9918 .9938 .9953 .9965 .9974 .9981 9987 .9990 .9993 .9995 .9997 .9998 .9998 .9999 .9999 1.0000 1.0000 2.6015 2.7011 .0011 N .3989 2.7 -2.6 .3085 .3446 3821 4207 4602 .5000 .5398 .5793 .6179 .6554 .6915 .7257 .7580 .4509 2.8 2.8008 -2.5 2 .5069 2.9 .0015 .0020 .0027 0037 2.9005 -2.4 .5668 3.0004 3.0 3.1 .6304 N 3.1003 .6978 w N -2.1 .7687 .0049 .0065 .0085 .0111 3.2002 3.3001 3.4001 .8429 -2.0 -1.9 -1.8 3.4 3.5 .7881 .9202 3.5001 .0143 1.0004 3.6 3.6000 > .0183 1.0833 3.7000 .0446 .0548 -1.6 -1.5 -1.4 .0232 .0293 .0367 .0668 .0808 .8159 .8413 .8643 .8849 9032 1.1 1.2 1.3 1.1686 1.2561 1.3455 3.8 3.9 4.0 3.8000 3.9000 4.0000