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.