Consider the following linear programming problem:

Maximize $401+302+603$

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

$121+82+1031500$

$x_1=20$

$x_{3}100$

$x_1,x_2,x_{3}0$

How many slack, surplus, and artificial variables would be necessary if the simplex algorithm were used to solve this problem?

Select one:

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

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

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

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