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 Remark If R is unbounded, then a maximum or a minimum value of the objective
function may not exist However, if it exists, it must occur at a corner point of R