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Math Help - maximization problem

  1. #1
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    maximization problem

    im not sure if this is the right forum to post this, if not please tell me where i should
    i have this problem :

    to find the ratio x/y for which the expression x*exp(-x) + y*exp(-x -y)
    is maximaized

    can anyone suggest how to do it ?

    thanks
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Find the maximum of


    \varphi (r)=\max \{f(ry,y):y\in\mathbb{R}\}
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  3. #3
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    thanks for the response, but can you please explain more ?
    i dont understand your answer
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  4. #4
    MHF Contributor FernandoRevilla's Avatar
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    The ratio is r=x/y. For every fixed r the function on the line x=ry is g(y)=f(ry,y) . For every r you will find a maximun (I hope), this maximum ( denote it by \varphi(r) ) depends on r . Now, find the maximum of \varphi .
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