Find the solution to the following Optimization problem using the simplex algorithm:

Write down the dual problem and give its solution.

$$\begin{aligned} & \text { maximise } 3 x_{1}+6 x_{2}+4 x_{3} \\ & \text { subject to } 2 x_{1}+3 x_{2}+x_{3} \leqslant 7 \text {, } \\ & 4 x_{1}+2 x_{2}+2 x_{3} \leqslant 5, \\ & x_{1}+x_{2}+2 x_{3} \leqslant 2, \quad x_{1}, x_{2}, x_{3} \geqslant 0 . \end{aligned}$$