Coefficient of Artificial Variable in Objective Function
The coefficient of an artificial variable in the objective function of a maximization problem is typically set to zero. This is done to ensure that the artificial variables do not influence the optimization process and only serve the purpose of helping in finding a feasible solution.

Explanation
- Objective Function: The objective function in a linear programming problem represents the quantity that needs to be maximized or minimized. It is a linear combination of decision variables and constants.
- Artificial Variables: Artificial variables are introduced in the initial tableau to help in finding an initial feasible solution for the linear programming problem. They are used when the constraints of the problem do not form a feasible region.
- Coefficient in Objective Function: The coefficient of an artificial variable in the objective function is typically set to zero because the goal is to minimize or maximize the actual objective of the problem, not the artificial variables. Setting the coefficient to zero ensures that the artificial variables do not impact the optimization process.
- Maximization Problem: In a maximization problem, the objective is to maximize the value of the objective function. The artificial variables are only used to help in finding a feasible solution, and their coefficients are set to zero in the objective function.
In conclusion, the coefficient of an artificial variable in the objective function of a maximization problem is set to zero to ensure that the optimization process focuses on maximizing the actual objective of the problem, rather than the artificial variables.