Simplex Method Tool

Finite mathematics utility: simplex method tool

Use of this system is pretty intuitive: Press "Example" to see an example of a linear programming problem already set up. Then modify the example or enter your own linear programming problem in the space below using the same format as the example, and press "Solve."

Notes

Do not use commas in large numbers. For instance, enter 100,000 as 100000.
The right-hand side of each constraint must be non-negative, so multiply through by-1 first if necesssary.
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
Decimal mode displays all the tableaus (and results) as decimals, rounded to the number of significant digits you select (up to 13, depending on your processor and browser).
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 simplex method tutorial) and displays the solution as fractions.
Mac users: you can use the inequality symbols "option+<" and "option+>" instead of "<=" and ">=" if you like (although some browsers may have difficulties with this).
Solution Display Some browsers (including some versions of Internet Explorer) use a proportional width font (like Geneva or Times) in text boxes. This will cause the display of solutions to appear a little messy. You can remedy this by changing the "Sans Serif" font in your browser preferences to "Courier" or some other fixed-width font, and then reloading the page.

Credits

Brent Dingle at Texas A&M University discovered and corrected an error in an older version of our algorithm.
Josh Purinton enhanced the utility: It will now accept multiletter variable names and equality contsraints.
Gabriel Balan at George Mason University has done extensive testing, and uncovered and diagnosed errors in earlier versions.
Thomas Dwyer III uncovered an error that could occur in an earlier version when there are multiple solutions.

Disclaimer: This page was created for educational purposes only. Its author is not responsible for any inaccuracies or errors in the results.