my question is: Find the dual to the problem: min $2y_1+3y_2+y_3$ s.t. $y_1+2y_2+y_3 \geq 2$, $y_1+y_2-y_3=1$, $y_2 \leq 0, y_3 \geq 0$
I'm really confused about the signs of the inequalities and variables. This is what I've done: max $2x_1+x_2$ s.t. $x_1+x_2=2$, $2x_1+x_2 \leq 3$, $x_1-x_2 \geq 1$, $x_1 \leq 0$, $x_2$ unrestricted in sign
Could someone tell me please whether or not my constraints in the dual are correct or whether they should be swapped? Also if anyone has any good tips for how to understand why the dual works then that'd be great!