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Math Help - maximise wrt w

  1. #1
    Newbie
    Joined
    Apr 2011
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    maximise wrt w

    having difficulty solving this:

    differentiate wrt to n first, then solve for it

    W = n[{10/[(n+1)]}^2] + 50[{(n)/(n+1)}^2]

    dw/dn ( i think gives):

    0= -200n/[{n+1}^3] + 100/[(n+1)^2] - 30 + 50(n^2) [-2/[(n+1)^3]] + 100n/((n+1)^2)

    then dont know how to solve for n?
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  2. #2
    Super Member

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    Lexington, MA (USA)
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    Hello, tickman!

    Differentiate wrt to n.

    . . W .= .n*[10/[(n+1)]^2 + 50*[{n/(n+1)]^2

    If I read the problem correctly, we have:

    . . . . . . . . . 100n . . . . . . 50n^2 . . . . . . . . . n^2 + 2n
    . . W . = . ------------ .+ .------------- . = . 50 . ------------
    . . . . . . . .(n + 1)^2 . . . (n + 1)^2 . . . . . . . .(n + 1)^2


    Now differentiate that . . .

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