Enter Model Data
This solver handles maximization models in the form: Maximize Z = c'x, subject to Ax ≤ b, x ≥ 0. It is most suitable when the initial tableau is dual-feasible and some right-hand sides are negative.
Example Data Table
Use this sample to test a tableau-friendly model.
| Model Part | x1 | x2 | x3 | Relation | RHS |
|---|---|---|---|---|---|
| Objective | 5 | 4 | 3 | Max | — |
| Constraint 1 | -2 | -1 | -1 | ≤ | -10 |
| Constraint 2 | -1 | -3 | -1 | ≤ | -12 |
| Constraint 3 | -1 | -1 | -2 | ≤ | -14 |
This example intentionally starts with negative right-hand sides, which is common when demonstrating the dual simplex approach.
Formula Used
The solver stores each tableau, updates the basis after every pivot, and reports final decision variables, slack variables, and the optimal objective value.
How to Use This Calculator
- Choose the number of variables and constraints.
- Enter objective function coefficients for each decision variable.
- Fill the constraint matrix coefficients and each right-hand side value.
- Use models written in maximization form with ≤ constraints and non-negative variables.
- Click Solve with Dual Simplex to generate the tableau sequence.
- Review the result panel above the form for the optimal values.
- Open the iteration details to inspect pivot history and basis movement.
- Export the summary with CSV or PDF buttons when needed.
Important Notes
Dual simplex works best when the initial tableau is dual-feasible but primal-infeasible. In practical terms, that often means the objective row is already acceptable, while one or more RHS values are negative.
If your model does not meet that structure, the solver may report that dual feasibility is not satisfied. In that case, reformulate the problem or generate a dual-simplex-ready tableau before solving.
FAQs
1. What does this calculator solve?
It solves linear programming maximization models using the dual simplex method and shows objective value, decision variables, slack variables, and tableau iterations.
2. When should I use dual simplex instead of primal simplex?
Use dual simplex when the starting tableau has infeasible RHS values but still preserves dual feasibility in the objective row.
3. Does this solver support negative right-hand sides?
Yes. Negative RHS values are often expected in dual simplex examples because the method repairs infeasibility step by step.
4. What problem format should I enter?
Enter a maximization model with ≤ constraints, non-negative variables, and coefficients arranged so the starting tableau is suitable for dual simplex.
5. Why might the calculator return a feasibility warning?
That usually means no valid pivot column exists or the objective row is not dual-feasible for the given tableau.
6. Are tableau iterations shown after solving?
Yes. Every stored tableau includes basis labels, row values, and the pivot note for deeper mathematical review.
7. Can I export the final results?
Yes. The page includes CSV export for structured data and PDF export for printable reporting.
8. Is this tool suitable for teaching and revision?
Yes. It helps students, teachers, and analysts inspect pivot logic, basis updates, and final solutions in one place.