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.

a) What price should NatBike charge each segment if there is no capacity constraint?

b) What price should NatBike charge each segment if the total available capacity is 20,000 bicycles?

c) What is the total profit in each case?