# Help with dual of a problem

Could anyone confirm me if I write the correct dual for my problem? The different sets confuse me a lot.

$$s$$ is the source node and $$t$$ the sink node.

I'm uncertain if the last dual constraint in necessary.

• Please use MathJax. You have a typo ($A3$ instead of $A^3$). Also, your primal problem doesn't mention $A^4$ anywhere. And do you have lower bounds $X_a \ge 0$? May 16 at 20:48
• Sorry that I missed the $A3$. $A^4$ is part of $A$, but is not in the objective function. It's in the "Notice that". May 16 at 20:51
• OK, thank you for the clarification. Two more typos: $x$ should be $X$, and $X_e$ should be $X_a$. May 16 at 21:03

• Your $$\le$$ dual constraints suggest that you omitted $$X_a \ge 0$$ in the primal. If instead $$X_a$$ is free, then your dual constraints should be $$=$$.