Q$5.$ Use the optimal primal solution for the maximization problem, given below to find the dual optimal solution using duality eoneepts $($complementary slackness and strong duality theorem :

Maximize $z=3x_1+2x_z.$

subject $to2x_1+x_{2}10.$

$x_1+x_{2}4,$

$-x_1+2x_{2}6,$

$x_{1}0,x_{2}0.$

$2u_1{x}^{u_2}$

Optimal primal solution: $x_i^{**}=2\mathrm{.}8,x_i^{**}=4\mathrm{.}4,$ with $z^{**}=17\mathrm{.}2$

HINT: where's' and $\text{'}e\text{'}$ are slack $($primal$)$ and surplus $($dual$)$ variables respectively

stet $x=\{x_2=,x_2\}$ be a feasible solution to the primat

$*$Let $u=\{u_y$dots,$u_n\}$ be a feasible solution to the dual

Then, $x$ is primal optimal and $u$ is dual optimal iff

$)=(1,2,$dotsm$)=(1,2,$dotsn

$(5$ Marks$)$