Chapter 3.1, Problem 39E

The regions A through G in the figure can be described by the inequalities

$\begin{array}{lll}x+3y\hfill & ?\hfill & 6\hfill \\ x+y\hfill & ?\hfill & 3\hfill \\ x-2y\hfill & ?\hfill & 2\hfill \\ x\hfill & \ge \hfill & 0\hfill \\ y\hfill & \ge \hfill & 0,\hfill \end{array}$

where ? can be either ≤ or ≥. For each region, tell what the ? should be in the three inequalities. For example, for region A, the ? should be ≥, ≤, and ≤, because region A is described by the inequalities

$\begin{array}{rrr}\hfill x+3y& \hfill \ge & \hfill 6\\ \hfill x+y& \hfill \le & \hfill 3\\ \hfill x-2y& \hfill \le & \hfill 2\\ \hfill x& \hfill \ge & \hfill 0\\ \hfill y& \hfill \ge & \hfill 0.\end{array}$