Please help with the problem:
A polyhedron P in $R^n$ is given by the system of m linear inequalities (of n variables). Furthermore, let P have k vertices (that is, k vectors satisfying all m constraints at least for n of which the equalities hold).
a) If m = 7; n = 2, might k be equal to: 0; 1; 7; 8; 23?
b) If m = 6; n = 3, might k be equal to: 0; 1; 6; 8; 9; 21?
c) If m = 8; n = 7, might k be equal to: 0; 1; 2; 7; 8; 9; 10?
d) If m = n = 6, might k be equal to: 0; 1; 2; 3?
e) If m = 4; n = 5, might k be equal to: 0; 1; 2?
Give an example if the answer is "yes" and explain why not if it is "no".