Where do we use the fact that we chose $b \geq 0$ in $P$ of the general primal-dual algorithm?

Question

It's in in the general primal-dual algorithm and I don't know why we choose $b \geq 0$ in $P$. I guess it may be related to the RP problem but I am not sure because I don't not have a deep understanding of it. Thanks a lot.

Starting with an LP standard form, which we call the primal problem $P$: \begin{align} \min z = c'\cdot x\\ Ax = b \geq 0\\ x\geq 0 \end{align}

Answer 1

If $b\ge 0$ then the solution $x=0$ is known to be valid.