Question $1($simplex algorithm$)$ Let us conider the following $(LP)$:

$(LP)\{\begin{array}{ccc}& \text{m}\text{a}\text{x}\text{i}\text{m}\text{i}\text{z}\text{e}& -3y_1-2y_2-y_3\\ & s.t& -y_1-y_2+y_{3}2\\ -2y_1-y_2-y_{3}6\\ y_1-y_2-y_{3}4\\ ,& y_{3}0.\end{array}$

Find the optimal value of this problem

$($i$)$ by bringing $($LP$)$ to standard form and applying the simplex algorithm using Tableu method

$($ii$)$ Computer task: Solve by applying Simplex algorithm of any package of $R$ or Pyhton or Matlab