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Homework Help: Lagrange Multiplier problem

  1. Nov 7, 2011 #1
    I'm in a bit of a hurry, so this isn't going to be very pretty.

    1. The problem statement, all variables and given/known data
    Maximize: V(l,d) = pi * (0.5*d)^2 * l
    Subject to: l + 3.5d = 84 -> C(l, d) = l + 3.5d - 84

    2. Relevant equations

    ∇V(l,d) = λ ∇C(l,d)

    3. The attempt at a solution

    ∇V(l,d) = 0.5*pi*d
    ∇C(l,d) = 0

    How do I find the Lagrange multiplier if the gradient of the condition-function is 0? I have to find the optimal conditions using Lagrange's method. I have already found the optimal conditions using the method involving elimination of variables, which gave me l = 28 and d = 26. Now I have to get the same results using this method.

    EDIT: Nevermind. I figured out my stupid mistake.
    Last edited: Nov 7, 2011
  2. jcsd
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