Use the mixed-contraint simplex method to maximize $$P = x_1+ 3 x_2 - 2 x_3$$ subject to $$\begin{array}{rrrrrrr} 2 x_1 & - & x_2 & - & 3 x_3 &\le & 4 \cr x_1 & + & 2 x_2 & + & x_3 &\ge & 3 \cr x_1 & - & 3 x_2 & - & 4 x_3 &\le & -5 \cr \end{array}$$
$$x_1 \ge 0\ \qquad x_2 \ge 0 \ \qquad x_3 \ge 0$$

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

$P =$