Build accurate pivot steps from any tableau. Review normalized rows, reduced costs, and RHS changes. Learn each transformation with neat outputs and useful exports.
Use manual mode to choose any pivot location. Use automatic mode to suggest the entering column from the most negative objective coefficient and the leaving row from the minimum positive ratio.
The calculator treats the last row as the objective row and the last column as the RHS column. In auto mode, the entering column is the most negative coefficient in the objective row. The leaving row is the smallest positive ratio from the eligible constraints.
This example is the same one loaded by the example button. It uses three constraints, five non-RHS columns, and one objective row.
| Row | x1 | x2 | s1 | s2 | s3 | RHS |
|---|---|---|---|---|---|---|
| R1 | 2 | 1 | 1 | 0 | 0 | 18 |
| R2 | 2 | 3 | 0 | 1 | 0 | 42 |
| R3 | 3 | 1 | 0 | 0 | 1 | 24 |
| Z | -3 | -2 | 0 | 0 | 0 | 0 |
For this example, a common first pivot is at row R3 and column x1, because x1 is the most negative objective coefficient and 24 ÷ 3 gives the minimum positive ratio.
A pivot operation changes the tableau basis. It makes the pivot element become 1 and turns every other entry in that pivot column into 0. This updates the system while preserving equivalence, allowing the algorithm to move toward a better feasible solution.
For a standard maximization tableau, the entering variable usually comes from the most negative coefficient in the objective row, excluding the RHS column. That column suggests the strongest immediate improvement in the objective value.
The leaving row is found with the minimum positive ratio test. Divide each eligible RHS by its positive pivot-column coefficient. The smallest positive ratio identifies the row that leaves the basis while keeping feasibility.
They are ignored because dividing by zero is invalid, and negative or zero coefficients do not produce the required bound for maintaining feasibility in the next basic solution. Only positive coefficients can define a valid leaving row.
Yes. Manual mode is useful for study, classroom checks, and verifying homework. You can choose any constraint row and any non-RHS column. The calculator then performs the exact row operations for that selected pivot location.
The graph compares the right-hand-side values for each constraint row before and after the pivot. It helps you see how the basis update changes the current basic solution and whether the transformed tableau shifts resource levels significantly.
The last row is assumed to be the objective row, and the last column is assumed to be the RHS column. This is the standard tableau structure used in many simplex examples and classroom formulations.
No. One pivot performs one simplex iteration. Many problems require several pivots before the objective row satisfies the stopping condition. This calculator focuses on one pivot step so you can inspect the transformation clearly.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.