Question #1 A publisher sells books to Borders at $12 each. Borders prices the book to its customers at $24 and expects demand over the next two months to be normally distributed, with a mean of 20,000 and a standard deviation of 5,000. Borders places a single order with the publisher for delivery at the beginning of the two-month period. Currently, Borders discounts any unsold books at the end of two months down to $3, and any books that did not sell at full price sell at this price.

a. Borders will consider this book to be a bestseller if it sells 25,000 copies. What is the probability that it is a bestseller?

b. Borders will consider this book to be a flop if it sells less than 50% of the mean forecast. What is the probability that it is a flop?

c. What is the probability that the book will sell within 20% of its mean forecast?

d. What order quantity maximizes Borders’ expected profit?

e. How much is this expected profit?

f. What is the corresponding fill rate?

g. How many books does Borders expect to sell at a discount?

h. The marginal production cost for the publisher is $1 per book. How much profit does the publisher make given Borders’ actions?

Question #2 [Refund Contract]

A movie studio sells the latest movie on DVD to Blockbuster at $10 per DVD. The marginal production cost for the movie studio is $1 per DVD. Blockbuster prices each DVD at $20 to its customers. DVD s are kept on the regular rack for a one-month period, after which they are discounted down to $5, Blockbuster places a single order for DVDs. Their current forecast is that sales will be normally distributed, with a mean of 10,000 and a standard deviation of 5,000.

a. How many DVDs should Blockbuster order?

b. What is its expected profit?

c. How many DVDs does it expect to sell at a discount?

d. What is the profit that the studio makes given Blockbuster’s actions?

A plan under discussion is for the studio to refund Blockbuster $4 per DVD that does not sell during the one-month period. As before, Blockbuster will discount them to $5 and sell any that remain.

e. Under this plan, how many DVDs should Blockbuster order?

f. What is the expected profit for Blockbuster?

g. How many DVDs are expected to be unsold at the end of the month?

h. What is the expected profit for the studio?

i. What should the studio do?

Question #3 [Revenue Sharing Contract]

Top Gun Records and several movie studios have decided to sign a revenue-sharing contract for DVDs. Each DVD costs the studio $2 to produce. The DVD will be sold to Top Gun for $3. Top Gun in turn prices a DVD at $15 and forecasts demand to be normally distributed, with a mean of 5,000 and a standard deviation of 2,000. Any unsold CDs are discounted to $1, and all sell at this price. Top Gun will share 35 percent of the revenue with the studio, keeping 65 percent for itself.

a. How may CDs should Top Gun order?

b. How many CDs should Top Gun expect to sell at a discount?

c. What is the profit that Top Gun expects to make?

d. What is the profit that studio expects to make?

Question #4 [Buy-Back Contract]

Tom owns an independent bookstore located in Philadelphia. Tom has to decide on the best order quantity for a new self-help book that is to be released soon. The books will each cost Tom $20 but will retail for $30. At the end of the season, Tom can dispose of all of the unsold copies of the book at $5 each. Tom estimates that demand can be represented by a normal distribution with mean 240 and a standard deviation of 100. The publisher’s cost per book is $7.

a. What order quantity maximizes Tom’s expected profit?

b. What is Tom’s expected profit?

c. What is the resulting profit for the publisher?

Now consider the supply chain to be a single (vertically-integrated) entity.

d. What quantity will maximize the supply chain’s profit?

e. How much is the total supply chain profit?

The publisher is proposing a buy-back arrangement: At the end of the season, they will buy back all unsold copies at $15.00. However Tom is responsible for shipping unsold copies back to the publisher at $1 per book.

f. What quantity should Tom order if he wishes to maximize his expected profit?

g. What is the resulting profit for the publisher?

h. What is the total profit for the supply chain?

Consider the question of the best buy-back price.

i. Compute the best buy-back price.

j. Compute the resulting profit for Tom under the best buy-back price.

k. Compute the resulting profit for the publisher under the best buy-back price.

l. What is the total profit for the supply chain now?

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