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Lagrange Multiplier theory question

  1. Aug 3, 2011 #1
    1. The problem statement, all variables and given/known data

    I made this up, so I am not even sure if there is a solution

    Let's say I have to find values for which these two inequality hold [tex]x^2 + y^5 + z = 6[/tex] and [tex]8xy + z^9 \sin(x) + 2yx \leq 200[/tex]

    And by Lagrange Multipliers that

    [tex]\nabla f = \mu \nabla g[/tex]

    So can I let [tex]f = 8xy + z^9 \sin(x) + 2yx - 200 \leq 0[/tex]?
  2. jcsd
  3. Aug 3, 2011 #2


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    Science Advisor

    What question are you trying to answer? Normally, the Lagrange multiplier method is used to find a maximum or minimum to a given function with some additional constraints. Here, you don't seem to have any function to maximize or minimize
  4. Aug 3, 2011 #3
    Yeah I made one by making f <= 0...?

    Okay I got this idea from another problem from this video

    go to 5:05....
    Last edited by a moderator: Sep 25, 2014
  5. Aug 3, 2011 #4

    Ray Vickson

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    Homework Helper

    I guess you want to know if it is possible to find some x,y,x that give you f(x,y,z) <= 0 and g(x,y,x) = 0, where f and g are the two functions given in your post. One way would be to solve the problem
    minimize f, subject to g = 0, then check if the min value of f is <= 0. This approach is pretty standard, for example, when checking if a set of linear equations and inequalities is feasible.

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