A publisher sells books to Barnes & Noble at $15 each. The marginal production cost for the publisher is $2 per book. Barnes & Noble prices the book at $26 and expects demand to be normally distributed with a mean of 25000 and a standard deviation of 6000. Barnes & Noble places a single order with the publisher. Currently, Borders discounts any unsold books down to $4 and any unsold books sell at this price.
How many books should Barnes & Noble order? What is their expected profit? How many books do they expect to sell at a discount?
If the publisher and Barnes & Noble are vertically integrated, what is the effect of “double marginalization” regarding the number of books to order and the supply chain profit?
A plan under discussion is to refund Barnes & Noble’s $5 per unsold book. As before Barnes & Noble will discount them to $4 and sell any that remain. Under this plan how many books will Barnes & Noble order? What is the expected profit for Barnes & Noble? How many books are expected to be unsold? What is the expected profit for the publisher? What should the publisher do?

Benetton has entered into a quantity flexibility contract for a seasonal product with its retailer. If the retailer orders O units, Benetton is willing to provide up to another 35 percent if needed. Benetton’s production cost is $24 and they charge the retailer a wholesale price of $40. The retailer prices to customers at $55 per unit. Any unsold units can be sold at a salvage value of $25 by the retailer. Benetton can only salvage $10 per unit for its left over inventory. The retailer forecasts demand to be normally distributed with a mean of 5000 and a standard deviation of 1800.
Q.How many units O should the retailer order?

NatBike, a bicycle manufacturer, has identified two customer segments, one that prefers a customized bicycle and is willing to pay a higher price and another that is willing to take a standardized bicycle but is more price sensitive. Assume that the cost of manufacturing either bicycle is $300. Demand from the customized segment has a demand curve of d1 = 20000−10p1 and demand from the price-sensitive standard segment is d2 = 40000−30p2. What price should NatBike charge each segment if there is no capacity constraint? What price should NatBike charge each segment if the total available capacity is 20000 bicycles? What is the total profit in each case?

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