Let $$f(x_1,x_2) = 4x_1+8x_2-x^2_1- x^2_2\ ; h = x_1+x_2-4$$ and $\lambda$ be Lagrangian multiplier

Lagrangian function L = f - $\lambda$h

L = $(x_1+8x_2$ $-$ $x^2_1$ $-$ $x^2_2)$ $--$ $\lambda$($x_1+x_2-4)$

L = $x_1+8x_2$ $-$ $x^2_1$ $-$ $x^2_2$ $-$ $\lambda$$x_1-\mathrm{\lambda}x_2+4\mathrm{\lambda}$ Conditions to find stationary points are $\frac{\partial L}{\partial x_1}$ = 0 …