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 X3 and the artificial variable X6.
- As the constraint 2 is of type '≥' we should add the surplus variable X4 and the artificial variable X7.
- As the constraint 3 is of type '≥' we should add the surplus variable X5 and the artificial variable X8.
| MINIMIZE: Z = 2 X1 + 1 X2 |  | MAXIMIZE: Z = -2 X1 -1 X2 + 0 X3 + 0 X4 + 0 X5 + 0 X6 + 0 X7 + 0 X8 |
subject to 50 X1 + 20 X2 ≥ 240030 X1 + 20 X2 ≥ 1800 10 X1 + 40 X2 ≥ 1200 | subject to 50 X1 + 20 X2 -1 X3 + 1 X6 = 240030 X1 + 20 X2 -1 X4 + 1 X7 = 1800 10 X1 + 40 X2 -1 X5 + 1 X8 = 1200 | |
| X1, X2 ≥ 0 | X1, X2, X3, X4, X5, X6, X7, X8 ≥ 0 |
We'll build the first tableau of Phase I from Two Phase Simplex method.