Use Table 13.4 Dan McClure owns a thriving independent bookstore in artsy New Ho
ID: 328939 • Letter: U
Question
Use Table 13.4
Dan McClure owns a thriving independent bookstore in artsy New Hope, Pennsylvania. He must decide how many copies to order of a new book, Power and Self Destruction, an exposé on a famous politician's lurid affairs. Interest in the book will be intense at first and then fizzle quickly as attention turns to other celebrities. The book's retail price is $18, and the wholesale price is $11. The publisher will buy-back the retailer's leftover copies at a full refund, but McClure Books incurs $3 in shipping and handling costs for each book returned to the publisher. Dan believes his demand forecast can be represented by a Normal distribution with mean 200 and standard deviation 70. 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. a. Dan will consider this book to be a blockbuster for him if it sells more than 375 units. Using Table 13.4 and the round-up function, what is the probability Power and Self Destruction will be a blockbuster? (Round your answer to 4 decimal places.) b. Dan will consider a book a “dog” if it sells less than 50% of his mean forecast. Using Excel, calculate the probability that this expose will be a dog. (Round your answer to 4 decimal places.) c. Use Table 13.4 to determine the probability that demand for this book will be within 20% of the mean forecast. (Round your answer to 4 decimal places.) d. Using Table 13.4 and the round-up rule, calculate the quantity that maximizes Dan’s expected profit. e. If Dan orders the quantity needed to achieve a 90% in-stock probability, then what is the probability that some customer won’t be able to purchase a copy of the book? f. Suppose Dan orders 275 copies of the book. Using Table 13.4 and the round-up method, calculate Dan's expected left-over inventory to a whole unit. Do not round intermediate calculations. g. Suppose Dan orders 275 copies of the book. What is Dan’s expected sales? Do not round intermediate calculations. h. Suppose Dan orders 275 copies of the book. What is Dan’s expected profit? Do not round intermediate calculations. i. Use Table 13.4 and the round-up function to determine how many books Dan should order if he wants to achieve a 90% in-stock probability. Do not round intermediate calculations. 7|3|2|3|3|1|5-5-9-7-7 6-9-3-8-4-1-8 2 4-5-6-7-8-9 3 2|2|2|2|2|2|2|3|3|3|3|3|3|3|3|3|3|4 3-5-7-8-8 1-7|2|6|9|1|3|5 7-7-8-8-8 7-8-8 | 5 | 6 | 7 | 8 | 9 | 0 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 90: 1. 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 4 th 20 1 5-6 8-6-5-4 6-3-9-6-4-2 5-6-6-7-8-9 2-4-6-9-3-6 3-3-3-4 5|7|0|1|9|3|3|9-2 (z 2 5-9 3-3-3-4-4 5-5-6-6-6-7. | 7 | 7 | 8 | 8 | 8-8 3 .2 1 | 0 9 | 8 | 7 | 6 | 5 | 4 3 2 1 0 1 | 2 3 4 5 6 7 | 8 | 9|01|23 .. -1|-1|-1|-1|-o-o-o-o-o-o-o-o-o 20 7-7-9-5-5-1-3-3|2|3|7 8-1-4|8|3|9-6 | 5 | 7 | 2 | 2 | 7 | 9 | 9 | 8 | 7 | 9 | 6 | 8 | 8 | 8 8 1|1|2|2|3|5|7|0|3|9 1|2|3 8-0-3-7 2 .O 9 | 8 | 7 | 6 5 4 3 2 1 | 0 | 9 | 8 | 7 | 6 | 5 4 3 2 103-87654.Explanation / Answer
(a) z-statistic for Dan's blockbuster threshold (375) = (375-200)/70 = 2.5
Using Table 13.4, F(z) = 0.9938 (this is the probability of selling less than 375)
Probability of selling more than 375 units = 1 - F(z) = 1-0.9938 = 0.0062
(b) 50% of forecast = 100 (this is Dan's threshold)
z-statistic = (100-200)/70 = -1.4286
Using excel, F(z) = NORMSDIST(-1.4286) = 0.0766
Probability that the expose will be a dog = 0.0766
(c) Upper limit of 20% of the mean = 200*(1+20%) = 240
z-statistic for 240 = (240-200)/70 = 0.5714
Using table 13.4, F(z=0.5714) = 0.7161 (using interpolation)
Lower limit of 20% of the mean = 200*(1-20%) = 160
z-statistic for 160 = (160-200)/70 = -0.5714
Using table 13.4, F(z=-0.5714) = 0.2838 (using interpolation)
Probability of selling between 160 and 240 = F(0.5714) = F(-0.5714) = 0.7161 - 0.2838 = 0.4323
(d) Underage cost, Cu = retail price - wholesale price = 18-11 = $ 7
Overage cost, Co = shipping and handling cost incurred for full refund of unsold copies = $ 3
Critical ratio = Cu/(Cu+Co) = 7/(7+3) = 0.7
Refer table 13.4, F-1(0.7257) = 0.6 (F(0.6) = 0.7257 value obtained by interpolation)
Using round-up rule, z = 0.6
Optimal order quantity = m + z*s = 200 + 0.6*70 = 242
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