X

PHPSimplex
Version 0.81

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

• Start
• Theory
• Example
• Help
• Exit

## 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 slack variable X21.
• As the constraint 2 is of type '≤' we should add the slack variable X22.
• As the constraint 3 is of type '≤' we should add the slack variable X23.
• As the constraint 4 is of type '≤' we should add the slack variable X24.
• As the constraint 5 is of type '≤' we should add the slack variable X25.
• As the constraint 6 is of type '=' we should add the artificial variable X29.
• As the constraint 7 is of type '=' we should add the artificial variable X28.
• As the constraint 8 is of type '=' we should add the artificial variable X27.
• As the constraint 9 is of type '=' we should add the artificial variable X26.
 MINIMIZE: Z = 10 X1 + 8 X2 + 8 X3 + 9 X4 + 8 X5 + 6 X6 + 7 X7 + 6 X8 + 7 X9 + 7 X10 + 6 X11 + 6 X12 + 5 X13 + 7 X14 + 6 X15 + 5 X16 + 6 X17 + 6 X18 + 6 X19 + 5 X20 MAXIMIZE: Z = -10 X1 -8 X2 -8 X3 -9 X4 -8 X5 -6 X6 -7 X7 -6 X8 -7 X9 -7 X10 -6 X11 -6 X12 -5 X13 -7 X14 -6 X15 -5 X16 -6 X17 -6 X18 -6 X19 -5 X20 + 0 X21 + 0 X22 + 0 X23 + 0 X24 + 0 X25 + 0 X26 + 0 X27 + 0 X28 + 0 X29 subject to 1 X1 + 1 X2 + 1 X3 + 1 X4 + 0 X5 + 0 X6 + 0 X7 + 0 X8 + 0 X9 + 0 X10 + 0 X11 + 0 X12 + 0 X13 + 0 X14 + 0 X15 + 0 X16 + 0 X17 + 0 X18 + 0 X19 + 0 X20 ≤ 10 X1 + 0 X2 + 0 X3 + 0 X4 + 1 X5 + 1 X6 + 1 X7 + 1 X8 + 0 X9 + 0 X10 + 0 X11 + 0 X12 + 0 X13 + 0 X14 + 0 X15 + 0 X16 + 0 X17 + 0 X18 + 0 X19 + 0 X20 ≤ 10 X1 + 0 X2 + 0 X3 + 0 X4 + 0 X5 + 0 X6 + 0 X7 + 0 X8 + 1 X9 + 1 X10 + 1 X11 + 1 X12 + 0 X13 + 0 X14 + 0 X15 + 0 X16 + 0 X17 + 0 X18 + 0 X19 + 0 X20 ≤ 10 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 X15 + 1 X16 + 0 X17 + 0 X18 + 0 X19 + 0 X20 ≤ 10 X1 + 0 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 + 0 X15 + 0 X16 + 1 X17 + 1 X18 + 1 X19 + 1 X20 ≤ 11 X1 + 0 X2 + 0 X3 + 0 X4 + 1 X5 + 0 X6 + 0 X7 + 0 X8 + 1 X9 + 0 X10 + 0 X11 + 0 X12 + 1 X13 + 0 X14 + 0 X15 + 0 X16 + 1 X17 + 0 X18 + 0 X19 + 0 X20 = 10 X1 + 1 X2 + 0 X3 + 0 X4 + 0 X5 + 1 X6 + 0 X7 + 0 X8 + 0 X9 + 1 X10 + 0 X11 + 0 X12 + 0 X13 + 1 X14 + 0 X15 + 0 X16 + 0 X17 + 1 X18 + 0 X19 + 0 X20 = 10 X1 + 0 X2 + 1 X3 + 0 X4 + 0 X5 + 0 X6 + 1 X7 + 0 X8 + 0 X9 + 0 X10 + 1 X11 + 0 X12 + 0 X13 + 0 X14 + 1 X15 + 0 X16 + 0 X17 + 0 X18 + 1 X19 + 0 X20 = 10 X1 + 0 X2 + 0 X3 + 1 X4 + 0 X5 + 0 X6 + 0 X7 + 1 X8 + 0 X9 + 0 X10 + 0 X11 + 1 X12 + 0 X13 + 0 X14 + 0 X15 + 1 X16 + 0 X17 + 0 X18 + 0 X19 + 1 X20 = 1 subject to 1 X1 + 1 X2 + 1 X3 + 1 X4 + 1 X21 = 10 X1 + 1 X5 + 1 X6 + 1 X7 + 1 X8 + 1 X22 = 10 X1 + 1 X9 + 1 X10 + 1 X11 + 1 X12 + 1 X23 = 10 X1 + 1 X13 + 1 X14 + 1 X15 + 1 X16 + 1 X24 = 10 X1 + 1 X17 + 1 X18 + 1 X19 + 1 X20 + 1 X25 = 11 X1 + 1 X5 + 1 X9 + 1 X13 + 1 X17 + 1 X29 = 10 X1 + 1 X2 + 1 X6 + 1 X10 + 1 X14 + 1 X18 + 1 X28 = 10 X1 + 1 X3 + 1 X7 + 1 X11 + 1 X15 + 1 X19 + 1 X27 = 10 X1 + 1 X4 + 1 X8 + 1 X12 + 1 X16 + 1 X20 + 1 X26 = 1 X1, X2, X3, X4, X5, X6, X7, X8, X9, X10, X11, X12, X13, X14, X15, X16, X17, X18, X19, X20 ≥ 0 X1, X2, X3, X4, X5, X6, X7, X8, X9, X10, X11, X12, X13, X14, X15, X16, X17, X18, X19, X20, X21, X22, X23, X24, X25, X26, X27, X28, X29 ≥ 0

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