Consider any linear programming model of $n$ variables and $m$ constraints which has multiple optimum solutions. If it is possible, I'd like to know the lower and upper limits (in terms of $n$, $m$ and possibly other elements as well) for the number of vertices from the feasible polyhedron that belongs to the set of optimum solutions.
I came to believe, that as long as the feasible polyhedron contains more than a single point, there would be at least 2 different vertices that belong to the set of optimum solutions. However, for the upper limit, I have no clue, except that the total number of vertices in a feasible polyhedron (which are not necessarily optimum) is at most $2^n$.
I'm not sure if my thoughts on this subject are correct, and maybe it's not possible to have a good estimation at all on this matter.