I'm doing an exercise in the book "Introduction to Linear Optimization" and be stuck in this problem. Can anyone here help me solve this. I really appreciate all your help.
Consider a polyhedron $P = \{x|Ax \ge b\}$. Given any $\epsilon \gt 0$, show that there exists some $\bar{b}$ with the following properties:
(a) The absolute value of every component of $b - \bar{b}$ is bounded by $\epsilon$
(b) Every basic feasible solution in the polyhedron $P = \{x|Ax \ge \bar{b}\}$ is nondegenerate.
Thanks so much.