If an artificial variable is present in the ‘basic variable’ column of optimal…

Answer: Infeasible

• Artificial variables are introduced (for example in Phase I of the two-phase method or via Big-M) to create an initial basic feasible solution for an auxiliary problem.

• Phase I minimizes the sum of artificial variables. If the Phase I optimal value is zero, all artificial variables can be eliminated and a feasible solution to the original LP exists.

• If at the end of Phase I any artificial variable remains basic with a positive value in the final tableau, the Phase I minimum is greater than zero, so the original constraints cannot be satisfied without the artificial variables.

• Therefore, the correct conclusion is that the original linear program is infeasible.

• Note: If an artificial variable is basic but has value zero and can be removed by pivoting without reintroducing artificials, a feasible basis for the original problem may still exist. The typical interpretation in exam questions is that a remaining artificial variable indicates infeasibility.