Revised Simplex Method Calculator
Revised simplex method calculator using matrix operations for efficient linear programming solving.
Simplex Calculator
How Simplex Method Calculator Works
Enter the LP Problem
Type the objective function coefficients and every constraint row with its right-hand-side value.
Choose Maximize or Minimize
Pick your optimization goal. The tool builds the initial tableau with slack variables automatically.
Run the Pivot Iterations
The calculator identifies pivot column by Cj-Zj, computes ratios, performs elementary row operations until optimal.
Read the Optimal Solution
Final tableau displays optimal variable values, Zj row, and the maximum/minimum objective value.
Sample Simplex Tableau Output
Example tableau iteration for a 2-variable maximization problem
| Basis | x1 | x2 | s1 | s2 | RHS | Cj-Zj |
|---|---|---|---|---|---|---|
| x1 | 14 | 0 | 0 | 1 | 14 | 0 |
| x2 | 7 | 1 | 0 | 0 | 7 | 5 |
| Zj | 35 | 5 | 0 | 0 | 35 |
The Matrix Form
The revised simplex method performs the same iterations as the standard method but stores only the basis inverse B⁻¹ rather than the entire tableau. The optimal basic solution is x_B = B⁻¹b, and reduced costs are computed from B⁻¹ as needed. This makes the revised method far more memory-efficient for large linear programs.
Why It Matters
For small textbook problems the standard tableau is fine, but real-world LPs have thousands of variables. The revised simplex method is the basis of professional LP solvers because it avoids storing and updating a huge tableau while producing identical optimal results.
Related calculators
Frequently Asked Questions
What is the revised simplex method?
The revised simplex method is a computationally efficient version of the simplex algorithm that updates the basis inverse matrix rather than the entire tableau, reducing calculation time for large LP problems.
How does the revised simplex calculator differ from the standard one?
Instead of calculating the whole tableau at every iteration, the revised calculator only computes the necessary pivot column and row using the current basis inverse, saving memory and computational effort.
Why use the revised simplex method?
It stores only the basis inverse instead of the full tableau, which saves memory and is faster for large linear programs.
Does it give the same answer?
Yes, the revised method produces exactly the same optimal solution as the standard tableau method.
What is B inverse used for?
The basis inverse is used to compute the current basic solution and the reduced costs at each iteration.