The optimal solution of a linear programming problem will always occur on a corner of the feasible region.

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The optimal solution of a linear programming problem will always occur on a corner or vertex of the feasible region. This is because the feasible region is a convex polyhedron formed by the intersection of half-spaces defined by the constraints. The objective function, which is a linear function, either increases or decreases as we move along any edge of the feasible region. Therefore, the minimum or maximum value of the objective function can only be achieved at a corner or vertex of the feasible region where two or more edges meet. This is known as the corner point theorem.

The Optimal Solution of a Linear Programming Problem Will Always