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Math Help - WOW!!!!

  1. #1
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    WOW!!!!

    Find producers' surplus at price level of p=$51 for price-supply equation below.

    p=S(x)=15+0.1x+0.0003x^2

    The producers' surplus is ______________
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  2. #2
    Senior Member DeMath's Avatar
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    Re: WOW!!!!

    First, find the root for x>0

    15+0.1x+0.0003x^2=51~\Rightarrow~x\approx217.752

    producers' surplus = \int_{0}^{217.752}[51-(15+0.1x+0.0003x^2)]\,dx=\ldots=4435.78 (Rounded to the nearest dollar, i.e. 4436)

    See the plot
    Last edited by DeMath; May 3rd 2012 at 08:29 PM.
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