The function P(x) = -30x^2 + 360x + 785 models the profit, P(x), earned by a theatre owner on the ba

Discussion in 'Calculator Requests' started by math_celebrity, Mar 6, 2017.

  1. math_celebrity

    math_celebrity Administrator Staff Member

    The function P(x) = -30x^2 + 360x + 785 models the profit, P(x), earned by a theatre owner on the basis of a ticket price, x. Both the profit and the ticket price are in dollars. What is the maximum profit, and how much should the tickets cost?

    Take the derivative of the profit function:
    P'(x) = -60x + 360

    We find the maximum when we set the profit derivative equal to 0
    -60x + 360 = 0

    Subtract 360 from both sides:
    -60x = -360

    Divide each side by -60
    x = 6 <-- This is the ticket price to maximize profit

    Substitute x = 6 into the profit equation:
    P(6) = -30(6)^2 + 360(6) + 785
    P(6) = -1080 + 2160 + 785
    P(6) = 1865
     

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