I would like to ask the community about some references on positive solutions of linear systems. A vector $v=(a_1,\ldots,a_n)$ is a positive solution of the linear system $AX=b$ if $Av^T=b$ and $a_i>0$ for all $i$. My question is:
What are positive solutions of a linear system good for?
I have seen a lot of interesting mathematics about such solutions and many other features of them (for example, on Roman's Advanced Linear Algebra), but I do not know a nice use of these solutions. Any reference on applications of positive solutions of linear systems would be very appreciated.