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Thread: Maximizing Linear Function

  1. #1
    Super Member sakonpure6's Avatar
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    Maximizing Linear Function

    If we have

    $\displaystyle f(x,y,z) = 3x + 2y +5z$

    Subject to the following constraints:

    $\displaystyle g(x,y,z) = x + 2y+z \leq 430$
    $\displaystyle h(x,y,z) = 3x+2z \leq 460$
    $\displaystyle i(x,y,z) = x+4y \leq 420$

    and we want to maximize (or minimize) it, how would we solve this? My lecture is originally about the Simplex method. But I was wondering, could we use Lagrange method here? I tried it but after finding partial derivatives of f(x,y,z) and the constraints I only come up with a solution to the scalar multiples of the constraints and I don't know what to do after that:

    $\displaystyle \nabla f(x,y,z) =\lambda \cdot g(x,y,z) + \theta \cdot h(x,y,z) + \eta \cdot i(x,y,z) $

    I get:

    $\displaystyle \lambda = 5 , \theta = 0 , \eta = -2$
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  2. #2
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    Re: Maximizing Linear Function

    The Lagrange method is for nonlinear optimisation, as it involves finding stationary points. Linear functions do not have these. You will need to use the Simplex Method.
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    Super Member sakonpure6's Avatar
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    Re: Maximizing Linear Function

    thank you Prove It
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