Secondary Constraints. Instead of solving a problem using all of its constraints, we can start by identifying the so-called secondary constraints. These are the constraints that we suspect are least restrictive in terms of the optimum solution. The model is solved using the remaining (primary) constraints. We may then add the secondary constraints one at a time. A secondary constraint is discarded if it satisfies the available optimum. The process is repeated until all the secondary constraints are accounted for.
Apply the proposed procedure to the following LP:
Maximize z = 5x1 + 6x2 + 3x2
Subject to
5x1 + 5x2 + 3x3 ≤ 50
X1 + x2 - x3 ≤ 20
7x1 + 6x2 - 9x3 ≤ 30
5x1 + 5x2 + 5x3 ≤ 35
12x1 + 6x2 ≤ 90
X2 - 9x3 ≤ 20
X1, x2, x3 ≥ 0