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Math Help - Optimization Problem

  1. #1
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    Optimization Problem

    I'm having trouble with this problem.

    A baseball team plays in a stadium that holds 58000 spectators. With the ticket price at $12 the average attendance has been 23000. When the price dropped to $10, the average attendance rose to 29000. Assume that attendance is linearly related to ticket price.


    What ticket price would maximize revenue?
    Last edited by MeganNix; March 11th 2010 at 07:27 PM. Reason: spelling and I did it wrong.
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  2. #2
    MHF Contributor chisigma's Avatar
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    On the basis of allowable data the 'average attendance' as function of the ticket price is represented in figure...



    ... and its value is with good approximation...

    E= 58\cdot 10^{3} - 3\cdot 10^{3}\cdot c (1)

    The expected revenue is...

    R = E\cdot c = 58\cdot 10^{3}\cdot c - 3\cdot 10^{3}\cdot c^{2} (2)

    ... and its derivative...

    \frac{dR}{dc} = 58\cdot 10^{3} - 6\cdot 10^{3}\cdot c (3)

    ... and it valishes for c= \frac{58}{6} \approx 9,67 $...

    Kind regards

    \chi \sigma
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  3. #3
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    Thanks, but that doesn't work. I have an online assignment that allows me to try as many times as I want to, and it doesn't allow that answer.

    And actually it was really close, so thank you for kinda leading me in the right direction. It ended up being $9.83
    Last edited by MeganNix; March 11th 2010 at 07:47 PM. Reason: I figured it out.
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