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Consider the following linear programming problem:

Maximize $40$ X$1+30$ X$2+60$X$3$

Subject to: X$1+$ X$2+$ X$3>=90$

$12$ X$1+8$ X$2+10$ X$3<=1500$

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$.$

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

d$.$

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