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Lagrange multiplier help

  1. Sep 13, 2009 #1
    ok this is just an example so you can see where im having problems with these(it isnt hw)

    i need to find the optimum values of X and Y

    U= XY

    m= Psuby(Y) + Psubx(X)

    the first order conditions are

    Y +u*Psubx

    X+ u*PsubY

    m= Psuby(Y) + Psubx(X)


    now , where im having problems is how do i find the optimum values from that. I know you are supposed to plug the FOC in but i cant get the answer my book shows me. could somebody walk me through that part?
     
  2. jcsd
  3. Sep 13, 2009 #2

    LCKurtz

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    It's hard to walk you through anything when you haven't stated the problem clearly. You need a function you want to optimize which I assume is U(x,y). Then you need a constraint equation which you haven't stated. Is it P(x,y) = 0? Next you make the auxiliary function:

    F(x,y) = U(x,y) + [tex]\lambda[/tex]P(x,y)
    using your formulas for U(x,y) and P(x,y).

    I have no idea what your m is and what you call your "first order conditions" aren't even equations; they are just expressions. The equations you need to set up and solve are

    F_x = 0
    F_y = 0
    F_[tex]\lambda[/tex] = 0

    Three equations in three unknowns.
     
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