Find an optimal solution to the linear programming problem

$$\max 3 x_{1}+2 x_{2}+2 x_{3}$$

in $x \geqslant 0$ subject to

$$\begin{gathered} 7 x_{1}+3 x_{2}+5 x_{3} \leqslant 44 \\ x_{1}+2 x_{2}+x_{3} \leqslant 10 \\ x_{1}+x_{2}+x_{3} \geqslant 8 \end{gathered}$$