Use the graphical method to maximize $$P = 4 x_1 + 7 x_2$$ subject to $$\begin{array}{rrrrr} 2 x_1 & + & x_2 & \le & 4 \cr x_1 & + & 2 x_2 & \le & 6 \cr \end{array}$$
$$x_1 \ge 0\ \qquad x_2 \ge 0$$

The maximum value is . Enter DNE if the maximum does not exist.