Part 1:
The GoGo Bunny is a hot toy this Christmas, and the manufacturer has decided to ration supply to all retailers. A large retail chain owns two channels-a discount channel and a high-service channel. The retailer plans to sell the toy at a margin of $4 in the discount channel and a margin of $8 in the high-service channel. The manufacturer sends 100,00GoGo Bunnies to the retailer. The retailer has forecast that the demand for the toy at the high-service channel is normally distributed, with a mean of 400,000 and a standard deviation of 150,000. How many toys should the retailer send to the high-service channel?
Part 2:
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 $200. Demand from the customized segment has a demand curve of d1=20,000 - 10p1 and the demand from the price-sensitive standard segment is d2=40,000-30p2. 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 20,000 bicycles? What is the total profit in each case?