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Math Help - Word problem

  1. #1
    Junior Member
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    Word problem

    Hi,

    I need some assistance with the following word problem :

    The profit P made by a cinema from selling x bags of popcorn can be modeled by:

    P = 2.36x - \frac{x^2}{25000} - 3500,   0 < x < 50000


    NOTE: the < is suppose to be also "or equal to" i just didn't know the syntax.

    I need to:

    a - Find the intervals on which [tex]P[/math is increasing and decreasing.

    b - If you owned the cinema, what price would you charge to obtain a maximum profit for popcorn? Explain please.
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  2. #2
    Super Member Random Variable's Avatar
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    solve  \frac {dP}{dx} = 0 to find the critical points
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  3. #3
    Junior Member
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    Right so I did this:

    P'=2.36-\frac{1}{12500}x = 0
    x = 29500



    and I tested in the intervals : (- infinity, 29500) , (29500, infinity) and found its increasing on the first and decreasing on the second (respectively).


    now how can I answer part b of my question ?
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  4. #4
    MHF Contributor
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    Talking

    If the profit value is increasing up to a certain x-value, and then decreasing after that x-value, where then would be the maximum value of P?
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