# Functions: K-T Condition

Consider the following program:

Maximize f(x,y)=x^2+4xy+y^2

subject to g(x,y)=x^2+y^2-1=0

https://brainmass.com/math/graphs-and-functions/functions-kuhn-tucker-condition-7945

#### Solution Preview

Solution. Let us denote the gradient vector of the function f(x,y) by Df(x,y). We rewrite the original program as follows.

Minimize F(x,y)=-f(x,y)=-x^2-4xy-y^2

. g(x,y)=x^2+y^2-1=0.

Since DF(x,y)=(-2x-4y,-4x-2y)', Dg(x,y)=(2x,2y)', by K-T ...

#### Solution Summary

A function is maximized using Kuhn-Tucker condition. The maximized function results are determined.

$2.19