Question

When many constraints are present in a linear optimization problem, there is a greater chance that a redundant constraint exists. Assume you are trying to maximize an objective function and you have two decision variables, X1 and X2. If a redundant constraint exists, does the constraint become necessary if you try to minimize (instead of maximize) the same objective function? Why? Do you need an objective function to determine if a constraint is redundant? Explain.

Answer 1

SOLUTION:-

A redundant constraint is that constraint which does not take participation is forming the feasibility region.

In other words,the boundaries of the feasibility region are not formed using this constraint.

This has got nothing to do with the objective.Whether it is minimisation or maximisation,the feasibility area does not change.

Therefore,the redundancy of constraint,as it depends only on the feasibility region,cannot also change with the change of objective.

We do not need an objective function to determine if a constraint is redundant.

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