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 surplus variable X5 and the artificial variable X9.
- As the constraint 2 is of type '≥' we should add the surplus variable X6 and the artificial variable X10.
- As the constraint 3 is of type '≥' we should add the surplus variable X7 and the artificial variable X11.
- As the constraint 4 is of type '≥' we should add the surplus variable X8 and the artificial variable X12.
| MINIMIZE: Z = 160 X1 + 80 X2 + 40 X3 + 120 X4 |  | MAXIMIZE: 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 ≥ 502 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 = 502 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 ≥ 0 | X1, 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.