Chapter 14.5, Problem 3CP

To determine

To calculate: The critical values x and y by setting the three partial derivatives $\frac{\partial F}{\partial x}$, $\frac{\partial F}{\partial y}$ and $\frac{\partial F}{\partial \lambda }$ equal of the objective function $F\left(x,y,\lambda \right)$ of the function $f\left(x,y\right)=x^2+y^2-4xy$ subject to the constraint $x+y=10$ equal to zero and then solving the equations simultaneously for x and y.