On R.W. Llewellyn's rules to identify redundant constraints: A detailed critique and some generalizations

In his book "Linear Programming" [1964]Llewellyn devoted a chapter to simplifications and reductions of a linear programming problem by means of algebraic rules. These rules are claimed to be rather general. Here we give some counterexamples, where the rules of Llewellyn do not hold. Furthermore we give some general rules to identify redundant constraints in the case Llewellyn considers and show that the original rules of Llewellyn together with an extra condition are a variant of these general rules. Finally we consider the question whether or not the rules of Llewellyn should be used to identify redundant constraints.