# Using Complementary slackness THM to check optimal solution for dual

I Have the following LP :

$\mathcal Min$ $z= 8x_1+4x_2+3x_3$

s.t.

$\mathcal 2x_1-x_2+x_3+x_4$ $\geq 1$ ($y_1$)

$\mathcal x_1+x_2-x_4$ $\geq 2$ ($y_2$)

$x_1$->$x_4$ $\geq 0$

I wrote the Dual for this problem and it's as follow :

$\mathcal Max$ $z=$ $y_1 +2y_2$

s.t.

$2y_1 + y_2 \leq 8$

$-y_1 + y_2 \leq 4$

$y_1 \leq 3$

$y_1 - y_2 \leq 0$

My question here is : Using the theorem of complementary slackness I want to demonstrate that $y_1 = 4/3$ & $y_2 = 16/3$ are optimal solutions for the dual problem.