$4\mathrm{.}6-3.$ Consider the following problem.

subject $to$

$x_1+4x_2+2x_{3}8$

$3x_1+2x_{2}6$

Minimize $Z=2x_1+3x_2+x_3,$

and

$x_{1}0,x_{2}0,x_{3}0.$

Introduce artificial variables to reformulate this problem as a convenient artificial problem

for preparing to apply the simplex method.