$($a$)$ Reformulate this problem as a convenient artificial problem for preparing to apply the

simplex method.

$($b$)$ Using the Big M method, work through the simplex method to solve the problem step

by step.

$($c$)$ Using the two$-$phase method, work through the simplex method to solve the $-$ Make right sides values to positive values if needed

$-$ Replace the unrestricted decision variable $1$with $(1$

$+1$

$)$ where

$1$

$+>=01$

$>=0$ problem

step by step.