Question $1(50$ points$)$:

Consider the primal problem below. With the aid of the sketches, show that degeneracy in the primal results in alternative optima in the dual. Determine the value of the primal$/$dual decision variables and the optimal solution for both using graphical method.

$Max{x}_1$

$s.t.$

$x_1+x_{2}3$

$x_1-x_{2}3$

$x_1,x_{2}0$