How the Calculator Works
The Simplex Method Calculator on this site is a client-side implementation of George Dantzig's simplex algorithm. When you enter an objective function and constraints, the tool parses the coefficients, converts the problem to standard form by adding slack variables (for less-than constraints), surplus variables (for greater-than constraints), and artificial variables where required, and then solves it using the Big M method so that less-than, greater-than, and equality constraints are all supported in a single objective.
At each iteration the calculator selects the entering variable from the most favourable Cj minus Zj value, applies the minimum-ratio test to choose the leaving variable, and performs the elementary row operations for the pivot. It records every tableau, including the Zj and Cj minus Zj rows, and stops when the optimality condition is reached. The tool also detects unbounded and infeasible problems and reports them explicitly rather than returning a misleading number.
How Results Are Verified
Every calculation runs entirely in your browser, so no data is sent to a server. The algorithm has been tested against textbook problems with known optimal solutions across maximization, minimization, two-phase, Big M, dual, and multi-variable cases to confirm that the reported optimal value and variable values are correct. For two-variable problems the same optimum can be confirmed independently with the graphical method, and for any problem the displayed tableau iterations let you reproduce and check each pivot by hand.
References
The methods implemented and explained on this site are based on standard operations-research literature:
- Dantzig, G. B. (1963). Linear Programming and Extensions. Princeton University Press.
- Hillier, F. S., & Lieberman, G. J. (2021). Introduction to Operations Research (11th ed.). McGraw-Hill.
- Taha, H. A. (2017). Operations Research: An Introduction (10th ed.). Pearson.
- Vanderbei, R. J. (2020). Linear Programming: Foundations and Extensions (5th ed.). Springer.
- Bertsimas, D., & Tsitsiklis, J. N. (1997). Introduction to Linear Optimization. Athena Scientific.