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PHPSimplex
Version 0.81

Copyright ©2006-2018. All rights reserved.

Developed by:
Daniel Izquierdo Granja
Juan José Ruiz Ruiz

English translation by:
Luciano Miguel Tobaria

French translation by:
Ester Rute Ruiz

Portuguese translation by:
Rosane Bujes

PHPSimplex

PHPSimplex


The problem is converted to canonical form by adding slack, surplus and artificial variables as appropiate (show/hide details)

MINIMIZE: Z = 160 X1 + 80 X2 + 40 X3 + 120 X4Conversion to canonical formMAXIMIZE: Z = -160 X1 -80 X2 -40 X3 -120 X4 + 0 X5 + 0 X6 + 0 X7 + 0 X8 + 0 X9 + 0 X10 + 0 X11 + 0 X12

subject to

3 X1 + 1 X2 + 2 X3 + 3 X4 ≥ 50
2 X1 + 1 X2 + 1 X3 + 2 X4 ≥ 36
1 X1 + 2 X2 + 2 X3 + 3 X4 ≥ 22
4 X1 + 3 X2 + 1 X3 + 1 X4 ≥ 120

subject to

3 X1 + 1 X2 + 2 X3 + 3 X4 -1 X5 + 1 X9 = 50
2 X1 + 1 X2 + 1 X3 + 2 X4 -1 X6 + 1 X10 = 36
1 X1 + 2 X2 + 2 X3 + 3 X4 -1 X7 + 1 X11 = 22
4 X1 + 3 X2 + 1 X3 + 1 X4 -1 X8 + 1 X12 = 120
X1, X2, X3, X4 ≥ 0X1, X2, X3, X4, X5, X6, X7, X8, X9, X10, X11, X12 ≥ 0

We'll build the first tableau of Phase I from Two Phase Simplex method.

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Direct Solution

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