Consider the following linear programming problem:

Maximize $40x_1+30x_2+60x_3$

Subject $to$: $x_1+x_2+x_{3}90$

$12x_1+8x_2+1031500$

$x_1=20$

$x_{3}100$

$x_1,x_2,x_{3}0$

How many slack, surplus, and artificial variables would be necessary if the simplex algo problem?

Select one:

a$.1$ slack, $2$ surplus, and $2$ artificial

b$.1$ slack, $2$ surplus, and $1$ artificial

c$.3$ slack, $6$ surplus, and $6$ artificial

d$.2$ slack, $1$ surplus, and $2$ artificial