When Z has an optimal value
(maximum or minimum), where the variables x and y are subject to constraints described
by linear inequalities, this optimal value must occur at a corner point* (vertex) of the
feasible region 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