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Optimize f(x,y,z) = x2 + y2 + z2 - 2x

  1. Oct 12, 2009 #1
    Optimize f(x,y,z) = x2 + y2 + z2 - 2x subject to the constraint g(x,y,z) = x2 + y2 + z2 - 25 = 0

    Step 1:
    L = f - [tex]\lambda[/tex]g = x2 + y2 + z2 - 2x - [tex]\lambda[/tex](x2 + y2 + z2 - 25).

    Step 2:
    Lx = 2x - 2 - 2[tex]\lambda[/tex]x = 0
    Ly = 2y - 2[tex]\lambda[/tex]y = 0
    Lz = 2z - 2[tex]\lambda[/tex]z = 0

    What do I do now? Please help.
     
  2. jcsd
  3. Oct 13, 2009 #2

    Office_Shredder

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    Re: Lagrange

    I see four equations and four unknowns (don't forget that g(x,y,z)=0 gives you another equation!). Have you tried solving for those unknowns?
     
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