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LeGrange multiplier with inequality

  1. Oct 18, 2009 #1
    1. The problem statement, all variables and given/known data
    Find the dimensions of the box with the largest volume, given the constraint that the perimeter of the cross sector perpendicular to length is at msot 108

    2. Relevant equations
    So I have f(x,y,z)=xyz
    and the constraint is 2x+2z<108

    3. The attempt at a solution
    I set up the legrange multipler <yz, xz, xy>=(multiplier)<2, 0, 2>
    So then you have
    and then 2x+2z<108
    But since xz=0(m), I can't figure out how to solve the 4 equations to get the possible points. If I have xz=0, then either x or z is 0, right? but then there would be no volume..any ideas? Thanks!
  2. jcsd
  3. Oct 18, 2009 #2


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    Science Advisor
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    Gold Member

    You probably have the problem stated incorrectly. As stated, the volume has no max because you could take y as large as you want no matter what x and z are.

    Re-read the problem. My guess is that it will say something like "the length of the box plus the perimeter" is bounded.
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