No feasible region

If the constraints contradict each other, their half planes have no common point, the feasible region is empty, and the problem has no feasible solution and so no optimal value.

Example: minimise Z = 3x + 2y with x + y ≥ 8, 3x + 5y ≤ 15, x, y ≥ 0. Under 3x + 5y ≤ 15 in the first quadrant, x + y is at most 5 (reached at (5, 0)), so it can never reach 8: nothing satisfies both.

Summary of the features seen: the feasible region is always convex; an optimal value, when it exists, sits at a corner; and when two corners tie, the whole edge between them is optimal.

Before tabulating, check the region is not empty; after tabulating, check whether it is bounded.