Chapter 5.3, Problem 39E

In Problems 39 and 40, 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.

$\begin{array}{l}\text{Minimize and maximize}\\ z=x-y\\ \text{subject to }x-2y\le 0\\ \text{ 2}x-y\le 6\\ x,y\ge 0\end{array}$