The simplex package is a collection of routines for linear optimization using the simplex algorithm as a whole, and using only certain parts of the simplex algorithm.

In addition to the routines feasible, maximize, and minimize, the simplex package provides routines to assist the user in carrying out the steps of the algorithm one at a time: setting up problems, finding a pivot element, and executing a single pivot operation.

To directly obtain a numerical solution to a linear program, it is recommended that you use the Optimization[LPSolve] command, which is more efficient for this purpose.

Each command in the simplex package can be accessed by using either the long form or the short form of the command name in the command calling sequence.

The following is a list of available commands:

To display the help page for a particular simplex command, see Getting Help with a Command in a Package.

The following is a list of conversions in the simplex package:

The following is a list of types that are limited to the simplex package:

$\mathrm{with}\left(\mathrm{simplex}\right)\:$

$\mathrm{cnsts}≔\left\{7x+4y+11z\le 30\,3x+4y-3z\le 23\,5x-4y-3z\le 10\right\}\:$

$\mathrm{obj}≔-x+y+2z\:$

$\mathrm{maximize}\left(\mathrm{obj}\,\mathrm{cnsts}\mathbf{union}\left\{0\le x\,0\le y\,0\le z\right\}\right)$

$\left\{x=0\,y=\frac{49}{8}\,z=\frac{1}{2}\right\}$

$\mathrm{maximize}\left(\mathrm{obj}\,\mathrm{cnsts}\,\mathrm{NONNEGATIVE}\right)$

$\left\{x=0\,y=\frac{49}{8}\,z=\frac{1}{2}\right\}$

$\mathrm{maximize}\left(\mathrm{obj}\,\mathrm{cnsts}\right)$

The implementation of the simplex algorithm is based on the initial chapters of:

Chvatal. Linear Programming. New York: W.H. Freeman and Company, 1983.