$4\mathrm{.}6-11.$ Consider the following problem.

Maximize $,Z=-x_1+2x_2+x_3,$

subject to

$3x_2+x_{3}120$

$x_1-x_2-4x_{3}80$

$-3x_1+x_2+2x_{3}100$

$($no nonnegativity constraints$).$

$($a$)$ Reformulate this problem so that all variables have nonnegativity constraints.

D$,$I $($b$)$ Work through the simplex method step by step to solve the problem.

C $($c$)$ Use a computer package based on the simplex method to solve the problem.