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I have a function F(x,y) and a constraint G(x,y), I am trying to maximize F but the normal Lagrange Multiplier method can't be solved analytically; it's too complicated, even for mathematica. Are there other strategies for doing this? Also I have an idea about the answer. Is it possible to prove this is a maximum through other means?

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    There is nothing that can be said in this generality. What kind of functions are $F$ and $G$?2012-09-26

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