# Lagrange Multiplier theory question

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

And by Lagrange Multipliers that

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

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

## Answers and Replies

HallsofIvy
Science Advisor
Homework Helper
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

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....

Last edited by a moderator:
Ray Vickson
Science Advisor
Homework Helper
Dearly Missed
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