A train company is considering applying yield management principles to its ticket sales. Suppose that there is no variable cost in the operation, only a fixed cost to run each train. The company decides that a student ticket will sell for half the cost of a business ticket. If demand for the business tickets is given by 50-3x where x is the sales price of a business ticket and demand for student tickets is given by 70-y^2 where y is the price of a student ticket how much should the company charge for tickets to maximize revenue?
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