$($b$)$ Consider the following LP model.

Maximize $Z=2x_1-x_2+x_3,$

subject $to$

$3x_1+x_2+x_{3}6$

$x_1-x_2+2x_{3}1$

$x_1+x_2-x_{3}2$

and

$x_{i}0,$ for $i=1,2,3$

$($ii$)$ A basic feasible solution to the above LP is $(0,0,\frac{1}{2},\frac{11}{2},0,\frac{5}{2}).$ Considering

the above LP as the primal, find the complementary dual solution to the given

basic feasible solution of the primal. Comment on its feasibility and optimality

$($i$.$e$.,$ whether it is suboptimal, or optimal, or super$-$optimal$)$ with proper

explanation.