Introduction:
In linear programming, the simplex method is an iterative procedure that helps to find the optimal solution for a linear programming problem. It involves selecting a variable to enter the basis and a variable to leave the basis. The variable to leave the basis is determined by finding the key element in the pivot row and column. In this article, we will discuss how to determine the leaving variable in the simplex method.

Key Column:
The first step in determining the leaving variable is to identify the key column. The key column is the column that corresponds to the variable that will enter the basis. To identify the key column, we need to look for the most negative coefficient in the objective row. If there are multiple negative coefficients, we select the column that corresponds to the variable with the most negative coefficient.

Key Row:
The next step is to identify the key row. The key row is the row that corresponds to the variable that will leave the basis. To identify the key row, we need to calculate the ratios of the constants in the right-hand column to the coefficients in the key column. The key row is the row with the smallest non-negative ratio.

Key Element:
Once we have identified the key row and key column, we need to find the key element. The key element is the element at the intersection of the key row and key column. This element will be used as the pivot element in the next iteration of the simplex method.

Conclusion:
In conclusion, the leaving variable in the simplex method can be determined by identifying the key column, key row, and key element. The key column corresponds to the variable that will enter the basis, the key row corresponds to the variable that will leave the basis, and the key element is the pivot element that will be used in the next iteration. By following these steps, we can continue to iterate until we find the optimal solution for the linear programming problem.