Please show the work/Math ( especially for c) Dan McClure owns a thriving indepe
ID: 379759 • Letter: P
Question
Please show the work/Math ( especially for c)
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 $20, and the wholesale price is $12. The publisher will buy back the retailer’s leftover copies at a full refund, but McClure Books incurs $4 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 a mean of 200 and a standard deviation of 80.
a.
Dan considers a book a “dog” if it sells less than 50 percent of his mean forecast. What is the probability this exposé is a “dog”?
b.
What is the probability that demand for this book will be within 20 percent of the mean forecast?
c.
What order quantity maximizes Dan’s expected profit?
a.
Dan considers a book a “dog” if it sells less than 50 percent of his mean forecast. What is the probability this exposé is a “dog”?
b.
What is the probability that demand for this book will be within 20 percent of the mean forecast?
c.
What order quantity maximizes Dan’s expected profit?
Explanation / Answer
a) 50% of mean forecast = 200*50% 100
z-stat = (100-200)/80 = -1.25
F(z) = NORMSDIST(z) = NORMSDIST(-1.25) = 0.1056 or 10.56 %
Therefore, probability this exposé is a “dog” = 10.56 %
b) upper bound of 20% of mean forecast = 200*(1+20%) = 240
z-stat = (240-200)/80 = 0.5
Corresponding F(z) = NORMSDIST(0.5) = 0.6914
lower bound of 20% of mean forecast = 200*(1-20%) = 160
z-stat = (160-200)/80 = -0.5
Corresponding F(z) = NORMSDIST(-0.5) = 0.3086
Probability that demand for this book will be within 20 percent of the mean forecast = 0.6914 - 0.3086 = 0.3828 or 38.28 %
c) Underage cost, Cu = retail - wholesale price = 20-12 = 8
Overage cost, Co = shipping and handling cost incurrent to return the unsold books = 4
Optimal service level, F(z) = Cu/(Cu+Co) = 8/(8+4) = 0.67
z-stat = NORMSINV(0.67) = 0.4307
Optimal order quantity that maximizes expected profit = mean + z * Std dev
= 200 + 0.4307 * 80
= 234