Given an integer program
Max c$^T$x
subject to Ax $\le$ b
$\quad\quad\quad\quad$ x$\in$Z$^+$
Show that if A and b are rational and there exists at least one feasible solution to the integer program and the linear programming relaxation is unbounded, then the integer program is also unbounded.
I'm honestly not sure where to start..I think I need to show that the linear program has some direction I can go in forever, and I can always get to an integer point somewhere along that direction since A and b are rational. Am I on the right track?