A movie theater estimates that for each. 50 increase in ticket price, the number of tickets sold decreases by 60. The current ticket price of 12.50 yields 1800 tickets sold. Set up an equation to represent the daily revenue. What price should the theater charge for tickets in order to maximize daily revenue?

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Mathematics

Torres

13 February, 22:59

A movie theater estimates that for each. 50 increase in ticket price, the number of tickets sold decreases by 60. The current ticket price of 12.50 yields 1800 tickets sold. Set up an equation to represent the daily revenue. What price should the theater charge for tickets in order to maximize daily revenue?

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Autumn Combs · Answer 1

R = revenue r = (12.50 + 0.5x) (1800 - 60x) r = - 30x2 + 150x + 22500r = - 30 (x2 - 150x - 750) r = - 30 (x - 30) (x + 25) {-25, 30} The zeros are - 25 and 30. The maximum occurs at 2.5. Since the price increases by 50 cent increments, the maximum would happen at x = 2 or x = 3The tickets can be either $13.50 or $14.00.