If the objective function is parallel to a constraint, the constraint is infeasible.

The statement is not necessarily true. If the objective function is parallel to a constraint, it doesn't automatically mean that the constraint is infeasible. Infeasibility in linear programming refers to a situation where no solution can satisfy all constraints simultaneously.

If the objective function is parallel to a constraint, it means that any point along that constraint line will yield the same value for the objective function. This could potentially lead to multiple optimal solutions if the constraint is part of the feasible region. However, it could also mean that there are no optimal solutions if the constraint is not part of the feasible region.

So, the feasibility of a constraint is determined by whether or not it forms part of the feasible region, not by its orientation relative to the objective function.