Lagrange Multiplier theory question

  • Thread starter flyingpig
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  • #1
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Homework Statement




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]?
 

Answers and Replies

  • #2
HallsofIvy
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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
 
  • #3
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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

Yeah I made one by making f <= 0...?

Okay I got this idea from another problem from this video


go to 5:05....
 
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  • #4
Ray Vickson
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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
 

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