For my economics/game theory thesis I need to optimize a function subject to an inequality constraint.(adsbygoogle = window.adsbygoogle || []).push({});

maximize f(x_{1}, x_{2}) = 1/(x_{1}+x_{2}+y_{1}+y_{2}-w) subject to g(x_{1}, x_{2}) = x_{1}+x_{2}+y_{1}+y_{2}< w

This isnt particularly important, but the x and y variables are quantity of production by a firm. The objective function given is the cost function, and its setup such that each additional unit of production is more costly. But for obvious reasons, the total quantity of production needs to be less than w or else the cost function would be positive.

This would be very easy to optimize with lagrange multipliers if the constraint was an equality, but I never learned how to optimize subject to an inequality. Ive looked up KKT conditions on wikipedia but it may as well be written in Greek (and for the most part, it is :D).

Can someone point me in the right direction for how to solve something like this?

EDIT: I gave the cost function so obviously it would make more sense to minimize. What my objective function ACTUALLY is is a profit function, which is why I said maximize.

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# Optimization subject to inequality constraint

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