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Consider the following linear programming problem:

Maximize $401+302+603$

Subject to: $,x1+x2+x390$

$121+82+1031500$

$x1=20$

$x3100$

$x1,x2,x30$

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

Select one:

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

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

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

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