The proofs of these theorems
are beyond the scope of the book Theorem 1 Let R be the feasible region (convex polygon) for a linear programming
problem and let Z = ax + by be the objective function 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