Given is $\max\left\{c^T \cdot x | Ax \leq b, x \geq 0\right\}$ which is a linear programming problem and its solution set $M$. Prove that you can find out in finite steps if $M$ is unbounded.
It will surely work using the Simplex algorithm but I'm not sure how to prove this correctly?
I think the same proof to this is: Prove that the Simplex algorithm will stop (in finite steps). It will stop in finite steps because there are finite number of feasible bases. In addition, every feasible basis determines a basic feasible solution with an objective value. To make sure that a feasible basis is never used more than once, one can strictly increase the objective value in every step. For this reason, the Simplex algorithm will come to an end in finite steps.
But I'm not sure if this is fine like that or if it's really a proof at all? :S