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Math Help - Langrange Multiplier Method

  1. #1
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    Langrange Multiplier Method

    Need help using the Lagrange Multiplier Method on this problem. I could easily optimize this with direct substitution but I need to know how to solve it using this method.

    z=f(x,y)=3(x-5)^2+4y+1307

    The Function is constrained by x+y=144

    so I have L(x,y)=3(x-5)^2+4y+1307-lambda(x+y-144)

    Then Lx(x,y)=6(x-5)-lambda=0
    Ly(x,y)=4-lambda=0
    g(x,y)=x+y-144=0

    am I going about this right?
    Last edited by Brokensound723; October 19th 2010 at 12:06 PM.
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  2. #2
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    Quote Originally Posted by Brokensound723 View Post

    z=f(x,y)=3(x-5)^2+4y+1307

    The Function is constrained by x+y=144

    so I have L(x,y)=3(x-5)^2+4y+1307-lambda(x+y-144)
    I get

    L(x,y,\lambda)=3(x-5)^2+4y+1307+\lambda (x+y-144)

    with

    L_x=6(x-5)+\lambda =0

    L_y=4+\lambda =0

    L_{\lambda}=x+y-144=0

    Now solve the system

    6(x-5)+\lambda =0 ...(1)

    4+\lambda =0 ...(2)

    x+y-144=0 ...(3)
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