Use the simplex method to solve the following simplex problems. \begin{aligned} &\text { a) Maximise }-5 x_{1}-x_{2}-3 x_{3} \text { subject to }\\ &-x_{1}+4 x_{2}+2 x_{3} \leq 0\\ &7 x_{2}+x_{3}

\leq 1\\ &-2 x_{1}+x_{2}-3 x_{3} \leq-2\\ &x_{1}, x_{2}, x_{3} \geq 0 \end{aligned} \begin{aligned} &\text { b) Maximise } 2 x_{1}+3 x_{2}+2 x_{3} \text { subject to }\\ &3 x_{1}+x_{2}+2 x_{3} \leq 6\\ &x_{1}+x_{2}+x_{3} \leq 4\\ &2 x_{1}+6 x_{2}+6 x_{3} \leq 20\\ &x_{1}, x_{2}, x_{3} \geq 0 \end{aligned}