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Math Help - More lagrange...

  1. #1
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    More lagrange...

    Hey

    Find max/min

    f(x,y,z) = xyz

    constraints x+y+z=5
    xy+yz+zx=7

    So I let g(x,y,z) = x+y+z-5
    h(x,y,z) = xy+yz+zx-7

    Then let Delta_f=lamda*Delta_g + mu*Delta_h .... and g(..) = 0 & h(..) = 0

    So the equations I got were:

    yz = lamda + mu(y+z)
    xz = lamda + mu(x+z)
    xy = lamda + mu(x+y)
    x+y+z=5
    xy+yz+zx=7

    With a bit of algebra, I got 3*lamda + 10*mu = 7

    but I'm a bit lost with the rest of the algebra to get critical points for x,y,z ?

    Anyone want to give it a shot? :]

    thanks!
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  2. #2
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    Quote Originally Posted by seekay View Post
    Hey

    Find max/min

    f(x,y,z) = xyz

    constraints x+y+z=5
    xy+yz+zx=7

    So I let g(x,y,z) = x+y+z-5
    h(x,y,z) = xy+yz+zx-7

    Then let Delta_f=lamda*Delta_g + mu*Delta_h .... and g(..) = 0 & h(..) = 0

    So the equations I got were:

    yz = lamda + mu(y+z)
    xz = lamda + mu(x+z)
    xy = lamda + mu(x+y)
    x+y+z=5
    xy+yz+zx=7

    With a bit of algebra, I got 3*lamda + 10*mu = 7

    but I'm a bit lost with the rest of the algebra to get critical points for x,y,z ?

    Anyone want to give it a shot? :]

    thanks!
    Instead of adding the three equations and using the constraits as you have, try subtracting the equations in pairs and factoring and see where that gets you.
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