Theorem 2 Let R be the feasible region for a linear programming problem,
and let Z = ax + by be the objective function If R is bounded, then the
objective function Z has both a maximum and a minimum value on R and
each of these occurs at a corner point (vertex) of R � If the feasible region is unbounded, then a maximum or a minimum may not
exist However, if it exists, it must occur at a corner point of R