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 X5.
- As the constraint 2 is of type '≤' we should add the slack variable X6.
- As the constraint 3 is of type '≤' we should add the slack variable X7.
| MAXIMIZE: Z = 50 X1 + 25 X2 + 20 X3 + 30 X4 |  | MAXIMIZE: Z = 50 X1 + 25 X2 + 20 X3 + 30 X4 + 0 X5 + 0 X6 + 0 X7 |
subject to 16 X1 + 4 X2 + 8 X3 + 12 X4 ≤ 64030 X1 + 5 X2 + 10 X3 + 20 X4 ≤ 900 2 X1 + 3 X2 + 1 X3 + 2 X4 ≤ 200 | subject to 16 X1 + 4 X2 + 8 X3 + 12 X4 + 1 X5 = 64030 X1 + 5 X2 + 10 X3 + 20 X4 + 1 X6 = 900 2 X1 + 3 X2 + 1 X3 + 2 X4 + 1 X7 = 200 | |
| X1, X2, X3, X4 ≥ 0 | X1, X2, X3, X4, X5, X6, X7 ≥ 0 |
We'll build the first tableau of the Simplex method.