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

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 S21, and the wholesale price is $14. The publisher will buy-back the retailer's leftover copies at a full refund, but McClure Books incurs $5 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 Dan will consider this book to be a blockbuster for him if it sells more than 385 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 0.0035 b. 0.0668 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 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 quaiytht aximizes Dan's expected profit. If Dan orders the quantity needed to achieve a 91% 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 not round intermediate calculations h. 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 i, should order if he wants to achieve a 91% in-stock probability. Do not round intermediate calculations

Explanation / Answer

(a) z-stat = (385-200)/70 = 2.6429 ~ 2.7 (using round-up function)

From table 13.4, F(z<=2.7) = 0.9965

Probability that the book will be a blockbuster, P(z >2.7) = 1-0.9965 = 0.0035

(b) 50% of demand forecast = 200*50% = 100

z-stat = (100-200)/70 = -1.4286

Using Excel, F(z<= -1.4286) = NORMSDIST(-1.4286) = 0.0766

Probability that the expose will be a dog = 0.0766

(c)

Upper bound of 20% of mean = 1.2*200 = 240

z-stat = (240-200)/70 = 0.5714 ~ 0.6 (using round-up rule)

Using table 13.4, F(z<=0.6) = 0.7257

Lower bound of 20% of mean = 0.8*200 = 160

z-stat = (160-200)/70 = -0.5714 ~ -0.6 (using round-up rule)

Using table 13.4, F(z<=-0.6) = 0.2743

Probability that the demand will be within 20% of mean = 0.7257 - 0.2743 = 0.4514

(d) Underage cost, Cu = Retail price - wholesale price = 21-14 = $ 7

Overage cost, Co = shipping and handling cost of returning unsold books = $ 5

Critical ratio F(z) = Cu/(Cu+Co) = 7/(7+5) = 0.5833

Using table 13.4, z = 0.3   (using round-up rule)

Optimal order quantity, Q = 200 + 0.3*70 = 221

I(z) = 0.5668

Expected leftover inventory, V = s*I(z) = 70*0.5668 = 40

Expected Sales, S = Q - V = 221 - 40 = 181

Expected profit = S*Cu - V*Co = 181*7 - 40*5 = $ 1067

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