Simplex Pivot Planning
A simplex tableau turns a linear program into rows of numbers. Each row shows one constraint. The final row shows the objective change. A pivot moves the solution from one corner point to another. The aim is better profit, lower cost, or another chosen target.
Why The Pivot Matters
The entering column tells which variable should grow next. The leaving row tells which basic variable must leave. The pivot element sits where that row and column meet. Dividing the pivot row by this element creates a leading one. Then each other row is cleaned to zero in that column.
Advanced Use Cases
This calculator is useful for classroom checks, tutoring pages, and planning notes. It accepts a full tableau, custom variable names, and custom basis names. You can run one pivot, choose a manual pivot, or continue through several iterations. Ratio tests help explain why a row leaves. Tableau history helps show every move.
Reading The Result
Look first at the selected entering variable. Then check the ratio table. Only rows with positive pivot column values can leave. The smallest nonnegative ratio wins. If no valid row exists, the model is unbounded under the selected rule. If no entering column exists, the tableau is optimal for the chosen direction.
Practical Tips
Use clean numbers when learning the method. Fractions can be entered as decimals. Keep the right side as the last column. Keep the objective row at the bottom. For a common maximization tableau, profit coefficients often appear as negative values in the objective row. Different textbooks may use different signs. Match the calculator setting to your tableau style.
Export And Review
The CSV button saves the calculated tableau for spreadsheets. The PDF button gives a compact report. Use both downloads when preparing assignments or review notes. The example table shows the expected layout. Replace it with your own data. Then inspect each pivot before trusting the final answer.
Limitations
This tool checks arithmetic and pivot logic. It does not prove your original model was written correctly. Confirm constraints, units, and objective direction first. Then use the result as a clear simplex pivot guide. Save each run, compare choices, and document every assumption before sharing answers clearly.