sci.op-research

In each iteration the simplex algorithm visit one of the possible corner
points. But what is the intuition behind this behaviour and why does it not
investigate a point somewhere in the middle of a line (assuming the number
of variables n 2 <= n <= 3)?

All corner points can be found by setting (m-n) variables = 0 and then
solving the remaining system. But I still don't see why this is necessary a
corner point.