Linear programming grapher
Simplex method tutorial
Topic summary
Review exercises
Linear programming grapherSimplex method tutorialTopic summaryReview exercisesWebmasterEspañol

Simplex method tool: v 2.0

This is version 2.0. The code is based on the simplex method as developed in the Waner and Costenoble textbooks and is available in GitHub under the terms of the MIT license. Reports of any errors or issues to the Webmaster will be greatly appreciated and acted on promptly. Use this link to return to the earlier version.

Use of this system is pretty intuitive. Press the "Examples" buttons to see how to format your linear programming problem.

  • This page also solves integer and mixed linear programing problems (using the "branch and bound" algorithm). To specify which variables are required to have integer values, use the format integer x,y,z (see the examples).
  • The utility is quite flexible with input. For instance, the following format will also be accepted (inequalities separated by commas):
    Maximize p = x+y subject to x+y <= 2, 3x+y >= 4
  • However, the numbers on the right-hand sides of all constraints must be non-negative.
  • Do not use commas in large numbers. For instance, enter 100,000 as 100000.
  • The simplex method assumes that all variables are nonnegative, so there is no need to enter inequalities like x>=0,y>=0, etc. (Including them just makes all the tableaus bigger and can slow things down.)
  • Decimal mode displays all the tableaus (and results) as decimals, rounded to the number of significant digits you select (up to 13).
  • Fraction mode converts all decimals to fractions and displays all the tableaus (and solutions) as fractions.
  • Integer Mode eliminates decimals and fractions in all the tableaus (using the method described in the tutorial on the simple method) and displays the solution as fractions.
  • Mac users: you can use the inequality symbols "option+<" and "option+>" instead of "<=" and ">=" if you like.

Disclaimer This software is for educational purposes only. Neither its authors nor Zweig Media LLC are liable for any special, incidental, indirect or consequential damages of any kind, or any damages whatsoever resulting from loss of use, data, or profits, whether or not advised of the possibility of damage, and on any theory of liability, arising out of or in connection with the use or performance of this software.