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I haven't had complete success with this either and may be using the wrong idea, but the idea I got from the book is that if you have two constraints, you can set $\nabla f = \lambda \nabla g + \mu \nabla h$.

Since the inequality gave the restricted region, I think we can just set it up as two equations, $h$ and $g$ to check along these functions. But here is where I stopped and planned to spend some more time today trying to solve this system of equations because it looks pretty crazy.

Hope someone will add more if I am not going about this right....

I haven't had complete success with this either and may be using the wrong idea, but the idea I got from the book is that if you have two constraints, you can set $\nabla f = \lambda \nabla g + \mu \nabla h$.h$. This is from 14.8, p. 381.

Since the inequality gave the restricted region, I think we can just set it up as two equations, $h$ and $g$ to check along these functions. But here is where I stopped and planned to spend some more time today trying to solve this system of equations because it looks pretty crazy.

Hope someone will add more if I am not going about this right....