Simplex Method Calculator : 3 Variables
Simplex method calculator for 3 variable linear programming problems. Solve LP problems with x1, x2, and x3 easily.
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.
Simplex Method Calculator : 3 Variables
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
How does the simplex method handle 3 variables?
For 3 variables, the simplex method uses a tableau with 3 decision columns (x1, x2, x3) plus slack variables. The pivot operations proceed exactly as in 2 variables, iterating until the optimal solution is found.
Can I graph 3 variable simplex problems?
Graphing 3 variables requires a 3D plot which can be visually complex. The simplex calculator bypasses the need for graphical methods by computing the exact algebraic iterations.