I have a problem in my book:
Maximize $ -x_1 + 2x_2$
$3x_1 +4x_2 \leq 12$
$ 2x_1-x_2 \geq 2 $
$x_1, x_2 \geq 0$
The problem asks to find the values of all the primal variables from the optimal dual solution.
So I figured first step is to find the dual which is:
Minimize $12y_1 - 2y_2$
$3y_1 - 2y_2 \geq -1$
$4y_1 + y_2 \geq 2$
I have confirmed this to be correct as solving both the primal and dual graphically produce the same result, that is $1.4545..$
I'm a bit confused what is being asked. Isn't the optimal dual solution the same as the optimal primal solution? We are also using different variables in the primal compared to the dual?
I'd much prefer an understanding of what is being asked in the question instead of a direct answer.
Thanks a lot.