# In linear programming, what does the primal problem imply about the sign of the dual variables?

In Bertsimas' Introduction to Linear Optimization, we define the primal problem in standard form as minimizing $$c'x$$ subject to $$Ax=b$$ and $$x\geq0$$, and the dual problem as maximizing $$p'b$$ subject to $$A^* p \geq c$$.

He makes the comment that this definition of the dual problem requires $$p_i$$ to have the same sign as that of $$a'_i x - b_i$$. I've gone back through the derivation of the dual problem and its constraints a few time, and am having trouble understanding why this is.

Any thoughts?

Thanks!

• A good explanation about transforming a primal problem into a dual problem can be found here by Mike Spivey – callculus Mar 11 at 20:23