# Lagrange Multiplier theory question

1. Aug 3, 2011

### flyingpig

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 $$x^2 + y^5 + z = 6$$ and $$8xy + z^9 \sin(x) + 2yx \leq 200$$

And by Lagrange Multipliers that

$$\nabla f = \mu \nabla g$$

So can I let $$f = 8xy + z^9 \sin(x) + 2yx - 200 \leq 0$$?

2. Aug 3, 2011

### HallsofIvy

Staff Emeritus
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. Aug 3, 2011

### flyingpig

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
4. Aug 3, 2011

### Ray Vickson

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