A primal linear program has constraints

$2x_1+x_{2}10$

$x_1+2x_{2}10$

$-x_1+2x_{2}6$

$x_1,x_{2}0$

$($a$)$One of many possible optimal solutions is $(x_1,x_2)=(2,2),$ but we cannot be sure if we do not

know the objective func$-$ tion.

b$.$ If the optimal solution of the linear program is at $(x_1,x_2)=(0,0),$ then the optimal solution of the

dual also has all decision variables equal to zero.

$($c$)$ For one given objective, the optimal solution could be at $(x_1,x_2)=(2,4)$ and at $,$

$\frac{10}{3}).$

$($d$)$ Depending on the objective, this linear program could be infeasible.