NatBike, a bicycle manufacturer, has identified two customer segments; one segment prefers a customized bicycle and is willing to pay a higher price whereas the other is willing to take a standardized bicycle but is more price sensitive.

Assume the customized bicycle costs $300 to manufacture, whereas a standardized bicycle costs $200 to manufacture.

Demand from the customized segment has a demand curve of d₁ = 20,000 - 10p₁ and demand from the standardized segment has a demand curve of d₂ = 40,000 - 30p₂.

Problem 1 (3 pts): Construct an optimization model to determine what price should NatBike charge each segment if there is no capacity constraint.

Problem 2 (2 pts): What price should NatBike charge each segment if the total available capacity is 20,000 bicycles?