Studying duality theory I have not found clear this point
considering the primal a minimize problem, if $x$ and $p$ are feasible solution to the primal and to the dual then $p^tb \leq c^tx$
for any vector $x$ and $p$ we define
$u_i=p_i(a^t_ix-b_i)$
$v_j=x_j(c_j-p^tA_j)$
for the definition of the dual problem the sign of $p_i $ must be the same of the sign of $(a^t_ix-b_i)$ and the sign of $ x_j$ must be the same of the sign of $(c_j-p^tA_j)$ so $u_i$ and $v_j$ are both $\ge 0$ ... etc
I don't understand why the sign must be the same and what these amounts mean.