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Lagrange multipliers

  1. Apr 20, 2010 #1
    1. The problem statement, all variables and given/known data
    Assume that the surface temperature distribution of an ellipsoid shaped object given by 4x2 + y2 + 4z2 = 16 is T(x,y,z) = 8x2 + 4yz - 16z + 600.


    2. Relevant equations



    3. The attempt at a solution
    I'm assuming we just have to find the maximum value of this function using the lagrange method.

    I started by writing the equation like this:

    8x2 + 4yz -16z + 600 - 4x2[tex]\lambda[/tex] - y2[tex]\lambda[/tex] - 4z2[tex]\lambda[/tex] + 16[tex]\lambda[/tex].

    Then I found the 4 partials and set them to 0:

    fx = 16x - 8x[tex]\lambda[/tex] = 0
    fy = 4z - 2y[tex]\lambda[/tex] = 0
    fz = 4y - 16 - 8z[tex]\lambda[/tex] = 0
    f[tex]\lambda[/tex] = -4x2 - y2 - 4z2 + 16 = 0

    My problem comes next when I try to solve this system of equations.
    When I solve them I get:
    x = 1 (or 0?)
    y = z = -(4/3)
    [tex]\lambda[/tex] = 2

    These don't check out.

    Does it looks like I'm going about this problem correctly? If so what am I doing wrong when solving the system of equations?
     
  2. jcsd
  3. Apr 20, 2010 #2
    ah nevermind it checks if I use x = 0.
     
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