Analyze constraints needing artificial variables online. Compare penalties, Phase One totals, and basis choices. Turn equations into organized simplex-ready rows with confidence today.
Use this tool to identify slack, surplus, and artificial variables for simplex preparation. It summarizes starting rows for Big M and Two Phase methods.
Choose a method, enter the objective coefficients, then fill up to four constraints. Use blank zero rows only when not needed.
This sample illustrates a mixed-constraint problem where both surplus and artificial variables are required.
| Item | Value |
|---|---|
| Objective | Maximize Z = 5x1 + 4x2 |
| Constraint 1 | 2x1 + x2 ≤ 18 |
| Constraint 2 | x1 + 2x2 ≥ 20 |
| Constraint 3 | 3x1 + x2 = 12 |
| Added Variables | s1, e1, A1, A2 |
| Phase One Start | W = A1 + A2 = 20 + 12 = 32 |
This calculator also normalizes rows with negative right-hand sides. It flips the inequality and multiplies the full row by negative one before adding auxiliary variables.
An artificial variable is a temporary helper variable used to start simplex iterations when a natural starting basis is unavailable. It is removed later from the final solution.
You usually need them for equality constraints and greater-than-or-equal constraints. Those rows cannot always create an identity basis using only slack or surplus variables.
Big M adds a large penalty directly into the objective function. Two Phase first minimizes the artificial variables, then solves the original objective after feasibility is established.
A negative right-hand side can complicate basis interpretation. Multiplying the row by negative one creates a cleaner standard form before slack, surplus, or artificial variables are added.
No. It prepares the constraint rows and starting artificial-variable analysis. Its main goal is to build a simplex-ready representation for study and setup.
It is the starting sum of artificial basis values after standardization. A zero value at the end of Phase One indicates that a feasible solution has been found.
Yes. The calculator accepts integer and decimal inputs for objective coefficients, constraint coefficients, the right-hand side, and the chosen Big M value.
The chart displays the initial artificial variable values by constraint. It helps you see which rows create feasibility penalties or contribute to the Phase One objective.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.