Scenario: American Airlines (AA) is trying to maximize profits across two kinds of travelers: vacationers (Group A) and business travelers (Group B). AA can effectively distinguish between the two types and can discriminate in pricing. Although fixed costs matter a lot for the calculation of profits, they do not matter for purposes of optimal pricing, so we'll ignore them for now; however, we cannot ignore marginal costs, which we will assume is a constant $100 per traveler. (For purposes of calculating total profit below, you can assume no fixed costs, for convenience.) Demand for each type of traveler is given by the following equations, where Qi and Pi is the quantity and price for type i:
QA = 1000 - 2PA
QB = 800 - PB
1. Again, assume AA can discriminate as above, but now the airline is constrained by the number of seats available: the maximum number of seats is 300. How should AA adjust to maximize profits?