Consider the following linear programming problem:Maximize $40$ X$1+30$ X$2+60$X$3$Subject to: X$1+$ X$2+$ X$39012$ X$1+8$ X$2+10$ X$31500$X$1,$ X$2,$ X$30.$How many slack, surplus, and artificial variables would be necessary if the simplex were used to solve this problem?Select one:a$\mathrm{.}1$ slack, $1$ surplus, and $1$ artificialb$\mathrm{.}3$ slack, $3$ surplus, and $3$ artificialc$\mathrm{.}1$ slack, $4$ surplus, and $4$ artificiald$\mathrm{.}1$ slack, $2$ surplus, and $2$ artificial