1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    HallsofIvy

    User Avatar
    Staff Emeritus
    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

    User Avatar
    Science Advisor
    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.

    RGV
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Lagrange Multiplier theory question
Loading...