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Larange multiplier

  1. Oct 27, 2009 #1
    1. The problem statement, all variables and given/known data

    Find mix/max

    2x + 6y + 10Z bounded by x^2 + y^2 + z^2 = 35

    After finding the partial derivative and letting it equal to the bounding equation * C

    2 = C * 2x
    6 = C * 2y
    10 = C * 2z

    x^2 + y^2 + z^2 = 35

    x = 1/C
    y = 3C
    z = 5C

    inputting this into the equation of sphere

    (1/C)^2 + (3C)^2 + (5C)^2 = 35

    =

    1/C^2 + 9C^2 + 25C^2 =35

    =

    1/C^2 + 34C^2 = 35

    now I tried a couple of different things and I think the simplest for I got it down to was
    this :
    1 = (35 - 34C^2) C^2

    It looks like C = plus/minus 1 from observation, but thats not deductive enough, and way
    to show it with math, and not just plugging it in please.

    From there If I find the constant C the I can try to find other variables , x, y, z
     
  2. jcsd
  3. Oct 27, 2009 #2

    lurflurf

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    2 = C * 2x
    6 = C * 2y
    10 = C * 2z
    so
    x = 1/C
    y = 3/C
    z = 5/C
    Then you will get a surprisingly nice answer, too nice in fact.
    if 1 = (35 - 34C^2) C^2 would have resulted without a mistake it is a quartic in quadratic form 34x^2-35x+1=(34x-1)(x-1)=0 where x=C^2
     
    Last edited: Oct 27, 2009
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