Problem $6$:

Consider the following LP$.$ The $x_i$ are choice variable $($outputs$)$ and the constraints are inputs.

max$=,2x_1+8x_2,$

$st{x}_1+x_2,10$

$x_2,5$

$x_1,=8$

$x_1,x_{2}0,$

Graph and solve for the optimal $x_j,s_i,$ and $.$