How to Find the Leaving Variable in Linear Programming

To find the leaving variable in a linear programming problem, you need to follow these steps:

1. Determine the pivot column: Look for the most negative (or positive, if maximizing) coefficient in the objective function row. This coefficient indicates the direction in which the objective function can be improved the most.

2. Determine the pivot row: Divide each element in the right-hand column (the ratio of the constant term to the corresponding coefficient in the pivot column) by the corresponding coefficient in the pivot column. The smallest positive ratio indicates the pivot row.

3. Determine the leaving variable: The leaving variable is the variable that corresponds to the pivot row. It is the variable that currently has a non-zero coefficient in the pivot column.

By following these steps, you can identify the leaving variable in a linear programming problem.