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Dan McClure owns a thriving independent bookstore in artsy New Hope, Pennsylvani

ID: 379982 • Letter: D

Question

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 $21, and the wholesale price is $13. The publishen will buy-back the retailers leftover copies at a full refund, but McClure Books incurs 53 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 150 and standard deviation 80 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. Dan will consider this book to be a blockbuster for him if it sells more than 365 and Self Destruction will be a blockbuster? (Round your answer to 4 decimal places.) Dan will consider a book a "dog" if it sells less than 50% of his mean forecast. a. units. Using Table 13.4 and the round-up function, what is the probability Power Using Excel, calculate the probability that this expose will be a dog (Round your answer to 4 decimal places.) Use Table 13.4 to determine the probability that demand for this book will be C. within 20% of the mean forecast. (Round your answer to 4 decimal places.) dUsing Table 13.4 and the round-up rule, calculate the quantity that maximizes Dan's expected profit. If Dan orders the quantity needed to achieve a 93% in-stock probability, then what e. is the probability that some customer won't be able to purchase a copy of the book? Suppose Dan orders 300 copies of the book. Using Table 13.4 and the round-up f. method, calculate Dan's expected left-over inventory to a whole unit. Do not round intermediate calculations Suppose Dan orders 300 copies of the book. What is Dan's expected sales? Do 9- not round intermediate calculations. Suppose Dan orders 300 copies of the book. What is Dan's expected profit? Do not round intermediate calculations. Use Table 13.4 and the round-up function to determine how many books Dan should order if he wants to achieve a 93% in-stock probability. Do not round intermediate calculations

Explanation / Answer

Table 13.4 is not given in the question. So this problem is solved using Excel

a) For selling quantity = 365, z-state = (365-150)/80 = 2.69

Value of F(z) = NORMSDIST(2.69) = 0.9964

Probability of selling more than 365 units = 1 - 0.9964 = 0.0036 or 0.36%

b) x = 50%*150 = 75

z-state = (75-150)/80 = -0.9375

Value of F(z) = NORMSDIST(-0.9375) = 0.1743

Probability of selling less than 75 copies = 0.1743 or 17.43 %  

c) upper limit = 150 + 150*20% = 180

z-state = (180-150)/80 = 0.375

F(z) = NORMSDIST(0.375) = 0.6462

lower limit = 150 - 150*20% = 120

z-state = (120-150)/80 = -0.375

F(z) = NORMSDIST(-0.375) = 0.3538

Probability of selling within 120 and 180 units = 0.6462 - 0.3538 = 0.2924   or 29.24  %

d) Underage cost, Cu = retail price - wholesale price = 21-13 = 8

Overage cost, Co = 3

Critical ratio = Cu/(Cu+Co) = 8/(8+3) = 0.7273

z-stat = NORMSINV(0.7273) = 0.6046

Optimal quantity that maximizes profit = mu + z*sigma

= 150 + 0.6046*80

= 198