(Solved): Solve the linear programming problem using the simplex method. Maximize \( \mathrm{M}=\mathrm{x}+3 ...

Solve the linear programming problem using the simplex method. Maximize \( \mathrm{M}=\mathrm{x}+3 \mathrm{y}+7 \mathrm{z} \) subject to \[ \begin{array}{l} x+2 z \leq 10 \\ 3 y+z \leq 24 \\ x, y, z \geq 0 \end{array} \] Find the solution. \[ x=y=, z=, M= \]