I am working on a problem where it would be nice to prove that the feasible region of a LP problem is bounded, but where it is not necessary to solve any particular problem.
In particular, given an NxN matrix $A$ and a non-negative vector $\vec{b}\in\mathbb{R}^N$, I would like to find a set of sufficient conditions to guarentee that the set of non-negative vectors $\vec{x}\in\mathbb{R}^N$ such that $A\vec{x}\leq\vec{b}$ is bounded.
Having no experience with linear programming, I am not sure where to even start and have been getting unnecessarily bogged down with details on the simplex algorithm - which aren't needed right now because I don't need a particular solution. Any references to literature focusing on this aspect of the LP problem would be very much appreciated!
Just in case anyone has a better idea of how to approach the problem I'm currently working, I'm trying to, given a N-dimensional quadratic form $Q:\mathbb{R}^N\rightarrow\mathbb{R}$, find a set of conditions guarenteeing that the set of non-negative vectors $\vec{x}\in\mathbb{R}^N$ such that the partial derivative of $Q$ in each direction is non-negative is bounded. This naturally turned into something like a LP problem, so I thought this would be the direction to head.