2-Phase Simplex Method Calculator
2-Phase simplex method calculator for LP problems with artificial variables. Solve Phase 1 and Phase 2 automatically.
Our simplex method calculator handles maximization, minimization, 2-phase, Big M, dual, and revised simplex variants. Enter your objective function and constraints, and the calculator performs every pivot operation automatically.
2-Phase Simplex Method 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 |
Frequently Asked Questions
When to use the 2-phase simplex method?
The 2-phase simplex method is used when the linear programming problem contains constraints with 'greater than or equal to' (≥) or 'equal to' (=) signs, requiring artificial variables to find an initial basic feasible solution.
How does the 2-phase simplex calculator work?
In Phase 1, the calculator minimizes the sum of artificial variables to find a feasible basis. If the minimum is zero, Phase 2 begins, dropping artificials and optimizing the original objective function.