Math

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An auditorium has 1600 seats. At a ticket price of $6, the owners can sell 1200 tickets. For each 25 cent increase in price the tickets sold reduces by 25. What price should the owners set to maximize the income?

  • Math -

    let the number of 25 cent increases by x
    income = ticket price x number of tickets sold

    income = (6+.25x)(1200-25x)
    = 7200 - 150x + 300x - 6.25x^2
    = -6.25x^2 150x + 7200

    d(income)/dx = -12.5x + 150 = 0 for a max of income
    12.5x = 150
    x = 12

    so the price for max income should be 6 + .25(12) = $9.00

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