Discussion
The optimal solution of the linear programming problem is located :
Answer: C
The optimal solution lies at one of the corners of the feasible region.
The feasible region of a linear programme is a convex polygon (polyhedron), and the objective function is linear. A linear function over such a region reaches its maximum or minimum at an extreme point, a vertex. That is the fundamental theorem of linear programming and the reason the simplex method moves from corner to corner.
An interior point or the centre can never be strictly better than a vertex. When a whole edge is optimal, its two end corners are optimal too, so 'on the surface' adds nothing beyond the corner statement.
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