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PHPSimplex
Version 0.81

Copyright ©2006-2024. 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

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## PHPSimplex

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

• As the constraint 1 is of type '=' we should add the artificial variable X21.
• As the constraint 2 is of type '=' we should add the artificial variable X20.
• As the constraint 3 is of type '=' we should add the artificial variable X19.
• As the constraint 4 is of type '=' we should add the artificial variable X18.
• As the constraint 5 is of type '=' we should add the artificial variable X17.
• As the constraint 6 is of type '=' we should add the artificial variable X16.
• As the constraint 7 is of type '=', and the independent term is negative (the constraint is multiplied by -1), we should add the artificial variable X15.
 MINIMIZE: Z = 12 X1 + 4 X2 + 3 X3 + 5 X4 + 5 X5 + 3 X6 + 2 X7 + 10 X8 + 10 X9 + 2 X10 + 10 X11 + 10 X12 + 2 X13 + 4 X14 MAXIMIZE: Z = -12 X1 -4 X2 -3 X3 -5 X4 -5 X5 -3 X6 -2 X7 -10 X8 -10 X9 -2 X10 -10 X11 -10 X12 -2 X13 -4 X14 + 0 X15 + 0 X16 + 0 X17 + 0 X18 + 0 X19 + 0 X20 + 0 X21 subject to 1 X1 + 1 X2 0 X3 0 X4 0 X5 0 X6 0 X7 0 X8 0 X9 0 X10 0 X11 0 X12 0 X13 0 X14 = 1-1 X1 0 X2 + 1 X3 + 1 X4 -1 X5 -1 X6 0 X7 0 X8 0 X9 0 X10 0 X11 0 X12 0 X13 0 X14 = 00 X1 -1 X2 0 X3 0 X4 0 X5 0 X6 + 1 X7 + 1 X8 -1 X9 -1 X10 0 X11 0 X12 0 X13 0 X14 = 00 X1 0 X2 0 X3 -1 X4 + 1 X5 0 X6 -1 X7 0 X8 0 X9 + 1 X10 + 1 X11 -1 X12 0 X13 0 X14 = 00 X1 0 X2 -1 X3 0 X4 0 X5 + 1 X6 0 X7 0 X8 0 X9 0 X10 -1 X11 + 1 X12 + 1 X13 0 X14 = 00 X1 0 X2 0 X3 0 X4 0 X5 0 X6 0 X7 -1 X8 + 1 X9 0 X10 0 X11 0 X12 0 X13 + 1 X14 = 00 X1 0 X2 0 X3 0 X4 0 X5 0 X6 0 X7 0 X8 0 X9 0 X10 0 X11 0 X12 -1 X13 -1 X14 = -1 subject to 1 X1 + 1 X2 + 1 X21 = 11 X1 -1 X3 -1 X4 + 1 X5 + 1 X6 + 1 X20 = 00 X1 + 1 X2 -1 X7 -1 X8 + 1 X9 + 1 X10 + 1 X19 = 00 X1 + 1 X4 -1 X5 + 1 X7 -1 X10 -1 X11 + 1 X12 + 1 X18 = 00 X1 + 1 X3 -1 X6 + 1 X11 -1 X12 -1 X13 + 1 X17 = 00 X1 + 1 X8 -1 X9 -1 X14 + 1 X16 = 00 X1 + 1 X13 + 1 X14 + 1 X15 = 1 X1, X2, X3, X4, X5, X6, X7, X8, X9, X10, X11, X12, X13, X14 ≥ 0 X1, X2, X3, X4, X5, X6, X7, X8, X9, X10, X11, X12, X13, X14, X15, X16, X17, X18, X19, X20, X21 ≥ 0

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