The feasible region

Each constraint is satisfied on a half plane: shade the side of its boundary line that passes a test point, usually (0, 0) when the line misses the origin.

The feasible region (or solution region) is the part of the plane common to every constraint, x ≥ 0 and y ≥ 0 included. Outside it lies the infeasible region.

Every point of the feasible region, on its boundary or inside, is a feasible solution: a plan that obeys all the limits. A point outside is an infeasible solution.

For the dealer, the region is the quadrilateral OABC with O(0, 0), A(20, 0), B(10, 50), C(0, 60). The plans (10, 50), (0, 60) and (20, 0) are feasible; (25, 40) is not, since 5 · 25 + 40 = 165 > 100.

An optimal solution is a feasible point at which Z takes its optimal value.

A feasible region is bounded if some circle can enclose it; otherwise it is unbounded, stretching without end in some direction.

The feasible region of a linear programming problem is always convex: the segment joining any two of its points stays inside it.