How do I find the Dual of the LP
min $ = 4y_1 +2y_2 - y_3 $
$s.t. y_1 + 2y_2 +2y_3 <= 6$
$s.t. y_1- y_2 + 2y_3 = 8$
$y_1, y_2 >= 0, y_3 $urs
How do I find the dual to this LP? What confuses me is the = sign. Also the urs variable. I'm not sure how to act on these.
Solution 1:
With the table below you do not need to transform $y_3$. You have to read the table from right to left, since the primal problem is min-problem. The dual of the LP is
$\texttt{max} \ \ 6u_1+8u_2$
$u_1+u_2\leq 4 \quad (y_1)$
$2u_1-u_2\leq 2 \quad (y_2)$
$2u_1+2u_2=8 \quad (y_3)$
$u_1\leq 0, u_2 \text{ unrestr.}$
