In Problem explain why Theorem 2 cannot be used to conclude that a maximum or minimum value exists. Graph the feasible regions and use graphs of the objective function z = x - y for various values of z to discuss the existence of a maximum value and a minimum value.
Minimize and maximize
z = x - y
subject to x - 2y ≤ -0
2x - y ≤ 6
x, y ≥ 0