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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]?