Use the mixed-constraint simplex method to minimize $$P = 2 x_1+ 2 x_2+ 2 x_3$$ subject to $$\begin{array}{rrrrrrr} 3 x_1 & - & x_2 & - & 7 x_3 &\le & - 12 \cr x_1 & + & 2 x_2 & + & 3 x_3 &\ge & 8 \cr x_1 & - & x_2 & + & 9 x_3 &\le & 10 \cr \end{array}$$
$$x_1 \ge 0\ \qquad x_2 \ge 0 \ \qquad x_3 \ge 0$$

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

$P =$

For the minimum value, enter the values of $x_1$, $x_2$, and $x_3$ in the spaces provided. If there are no solutions, you may leave these answers blank.

$x_1 =$

$x_2 =$

$x_3 =$