Math Calculus

A baseball team plays in a stadium that holds 58000 spectators. With the ticket price at $11 the average attendance has been 22000. When the price dropped to $10, the average attendance rose to 29000. Assume that attendance is linearly related to ticket price.

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  1. is there a question in there somewhere?
    Let x be the number of $1 price decreases. Then the attendance is
    22000 + 7000x
    That means the revenue is
    r(x) = (11-x)(22000+7000x) = -1000(7x^2-55x-242)
    dr/dx = -1000(14x-55)
    maximum revenue occurs at the vertex, when x = 55/14 = 3.92
    That is, max revenue of $350,036 is when the price is reduced to $8.08 and the attendance is 49,300

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