Leaving variable in the simplex method can be determined Ops: A. O corresponding to key column B. O corresponding to key row C. O coresponding to key element D. None of tese?

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Leaving Variable in the Simplex Method

Simplex method is a widely used algorithm in linear programming to solve optimization problems. It involves finding the optimal solution by iteratively moving from one feasible solution to another. In each iteration, a variable is chosen to enter the basis while another variable is chosen to leave the basis. This process continues until an optimal solution is obtained. In this article, we will discuss how to determine the leaving variable in the simplex method.

Key Column

First, we need to identify the key column. The key column is the column that contains the most negative coefficient in the objective function row. If there are multiple columns with negative coefficients, we choose the one with the smallest ratio of the constant term to the coefficient. This column will be the entering variable.

Key Row

Next, we need to find the key row. The key row is the row that has the smallest non-negative ratio of the constant term to the corresponding coefficient in the key column. This row will be the leaving variable.

Key Element

The key element is the element in the key row and key column. It is the pivot element that is used to perform row operations and transform the matrix to the next iteration. The key element is usually normalized to 1 by dividing the entire key row by the key element.

Conclusion

In conclusion, determining the leaving variable in the simplex method involves finding the key column, key row, and key element. The key column is the entering variable, while the key row is the leaving variable. The key element is used to perform row operations and transform the matrix to the next iteration. By iterating this process, we can find the optimal solution to the linear programming problem.

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