I have a very simple linear programming problem with the following constraints:
Minimize $3x_1 + 2x_2 - 33x_3$
subject to
$x_1 - 4x_2 + x_3 \leq 15$
$9x_1 + 6x_3 \leq 12$
$5x_1 + 9x_2 \geq 3$
$x1,\ x2,\ x3 \geq 0$
Simple enough. When I optimize using GAMS I get a minimum optimal solution of $-65.33$. I know the dual of this problem must have the same optimal solution. I got the dual by putting the above constraints into a matrix and taking the transpose of the matrix to get the new constraints as follows:
maximize $15y_1 + 12y_2 + 3y_3$
subject to
$y_1 + 9y_2 + 5y_3 \geq 3$
$-4y1 + 9y3 \geq 2$
$y1 + 6y2 \leq -33$
$y1,y2,y3 \geq 0$
When I run this optimization problem using GAMS I get an infeasible solution. Am I taking the dual of the original problem correctly? What am I missing in these new constraints?
Thanks in advance.