Use the mixed-constraint simplex method to maximize $$P = 8 x_1 + 4 x_2$$ subject to $$\begin{array}{rrrrr} x_1 & + & x_2 & \ge & 11 \cr 2 x_1 & + & 3 x_2 & \ge & 30 \cr x_1 & + & 4 x_2 & \le & 37 \cr \end{array}$$
$$x_1 \ge 0\ \qquad x_2 \ge 0$$

If there are no solutions, enter None for $P$.

Maximum value is $P =$

where $x_1=$

and $x_2=$