Non-Standard Simplex Method Calculator
Non-standard simplex method calculator for problems with greater-than or equal constraints, solved using the Big M method.
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 |
What Makes a Problem Non-Standard
A standard maximization problem has only less-than-or-equal constraints and non-negative right-hand sides. A non-standard problem contains greater-than-or-equal or equality constraints, which need surplus and artificial variables. This non-standard simplex method calculator adds those variables and solves the problem with the Big M method so any constraint type is supported.
Solving Non-Standard LPs
Greater-than constraints subtract a surplus variable and add an artificial variable; equality constraints add an artificial variable. The Big M penalty forces the artificial variables out of the basis, after which the calculator continues normal simplex iterations to the optimal solution and reports whether the problem is feasible.
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Frequently Asked Questions
What is a non-standard linear programming problem?
A non-standard problem has greater-than-or-equal or equality constraints (or a mix of constraint types), unlike a standard problem that has only less-than-or-equal constraints.
How are non-standard problems solved?
By adding surplus and artificial variables and using the Big M method or the two-phase method to remove the artificial variables and reach the optimum.
Why are artificial variables needed?
Greater-than and equality constraints have no obvious starting basic feasible solution, so artificial variables provide one and are then driven out of the basis.
Can a non-standard problem be infeasible?
Yes. If an artificial variable remains basic with a positive value at optimality, the constraints cannot all be satisfied and the problem is infeasible.
Does this calculator handle mixed constraints?
Yes, it accepts less-than, greater-than, and equality constraints together and solves them automatically.