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 atfirst and then fizzle quickly as attention turns to other celebrities. The book’s retail priceis $20, and the wholesale price is $12. The publisher will buy back the retailer’s leftovercopies at a full refund, but McClure Books incurs $4 in shipping and handling costsfor 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 will consider this book to be a blockbuster for him if it sells more than 400 units.What is the probability that Power and Self-Destruction will be a blockbuster? b. Dan considers a book a “dog” if it sells less than 50 percent of his mean forecast. Whatis the probability this exposé is a “dog”? c. What is the probability that demand for this book will be within 20 percent of themean forecast? d. What order quantity maximizes Dan’s expected profit? e. If Dan orders the quantity needed to achieve a 95 percent in-stock probability, what isthe probability that some customer won’t be able to purchase a copy of the book? f. Suppose Dan orders 300 copies of the book. What is Dan’s expected leftover inventory?g. Suppose Dan orders 300 copies of the book. What are Dan’s expected sales? h. Suppose Dan orders 300 copies of the book. What is Dan’s expected profit? i. How many books should Dan order if he wants to achieve a 95 percent in-stockprobability?
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 atfirst and then fizzle quickly as attention turns to other celebrities. The book’s retail priceis $20, and the wholesale price is $12. The publisher will buy back the retailer’s leftovercopies at a full refund, but McClure Books incurs $4 in shipping and handling costsfor 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 will consider this book to be a blockbuster for him if it sells more than 400 units.What is the probability that Power and Self-Destruction will be a blockbuster? b. Dan considers a book a “dog” if it sells less than 50 percent of his mean forecast. Whatis the probability this exposé is a “dog”? c. What is the probability that demand for this book will be within 20 percent of themean forecast? d. What order quantity maximizes Dan’s expected profit? e. If Dan orders the quantity needed to achieve a 95 percent in-stock probability, what isthe probability that some customer won’t be able to purchase a copy of the book? f. Suppose Dan orders 300 copies of the book. What is Dan’s expected leftover inventory?g. Suppose Dan orders 300 copies of the book. What are Dan’s expected sales? h. Suppose Dan orders 300 copies of the book. What is Dan’s expected profit? i. How many books should Dan order if he wants to achieve a 95 percent in-stockprobability?
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 atfirst and then fizzle quickly as attention turns to other celebrities. The book’s retail priceis $20, and the wholesale price is $12. The publisher will buy back the retailer’s leftovercopies at a full refund, but McClure Books incurs $4 in shipping and handling costsfor 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 will consider this book to be a blockbuster for him if it sells more than 400 units.What is the probability that Power and Self-Destruction will be a blockbuster? b. Dan considers a book a “dog” if it sells less than 50 percent of his mean forecast. Whatis the probability this exposé is a “dog”? c. What is the probability that demand for this book will be within 20 percent of themean forecast? d. What order quantity maximizes Dan’s expected profit? e. If Dan orders the quantity needed to achieve a 95 percent in-stock probability, what isthe probability that some customer won’t be able to purchase a copy of the book? f. Suppose Dan orders 300 copies of the book. What is Dan’s expected leftover inventory?g. Suppose Dan orders 300 copies of the book. What are Dan’s expected sales? h. Suppose Dan orders 300 copies of the book. What is Dan’s expected profit? i. How many books should Dan order if he wants to achieve a 95 percent in-stockprobability?
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 will consider this book to be a blockbuster for him if it sells more than 400 units. What is the probability that Power and Self-Destruction will be a blockbuster? b. 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”? c. What is the probability that demand for this book will be within 20 percent of the mean forecast? d. What order quantity maximizes Dan’s expected profit? e. If Dan orders the quantity needed to achieve a 95 percent in-stock probability, what is the probability that some customer won’t be able to purchase a copy of the book? f. Suppose Dan orders 300 copies of the book. What is Dan’s expected leftover inventory? g. Suppose Dan orders 300 copies of the book. What are Dan’s expected sales? h. Suppose Dan orders 300 copies of the book. What is Dan’s expected profit? i. How many books should Dan order if he wants to achieve a 95 percent in-stock probability?
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
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