Linear Programming Calculator Using Simplex Method
Free online linear programming calculator using the simplex method to solve LP problems step by step.
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 |
Linear Programming Online
This linear programming calculator uses the simplex method to solve LP problems of any size. Enter a linear objective and a set of linear constraints (≤, ≥, or =) and it returns the optimal value plus the value of every decision variable, showing each simplex iteration along the way.
Maximization and Minimization
The solver handles both directions and all constraint types using slack, surplus, and artificial variables as needed. It is suitable for coursework in operations research, management science, and quantitative methods.
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Frequently Asked Questions
How to calculate simplex method in linear programming?
Set up the initial simplex tableau with decision variables and slack variables. Identify the most negative Cj-Zj value as pivot column, calculate ratios to find pivot row, then perform elementary row operations to iterate.
Can this calculator solve any linear programming problem?
Yes, it handles standard maximization, minimization, and problems requiring the Big M or 2-phase methods by automatically adjusting the algorithm to fit your specific constraints.
What types of LP problems can it solve?
It solves both maximization and minimization linear programs with any mix of less-than, greater-than, and equal constraints.
Is there a limit on variables or constraints?
No fixed limit; the simplex method works for any number of decision variables and constraints.
Does it show the working?
Yes, every simplex tableau is displayed so you can follow each iteration to the optimal solution.