A simplified rule based on the individual changes D1, D2,..., and Dm in the right - hand side of the constraints can be used to test whether or not simultaneous changes will maintain the feasibility of the current solution. Assume that the right-hand side bi of constraint i is changed to bi + Di one as a tune, and that pi ≤ Di ≤ qi is the corresponding feasibility rang obtained by using the procedure in Section 3.6.2 by definition, we have pi ≤ 0 (qi ≥ 0) because it represents the maximum allowable decrease (increase) in bi. Next, define r1 to equal Di/Pi if Di is negative and Di/qi if Di is positive. By definition, we have 0 ≤ ri ≤ 1. The 100% rule thus says that, given the changes D1, D2,..., and Dm, then a sufficient (but not necessary) condition for the current solution to remain feasible is that r1 + r2 + ... + rm ≤ 1. If the condition is not satisfied, then the current solution may or may not remain feasible. The rule is not applicable if D1 falls out-side the range (pi, qi). In reality, the 100% rule is too weak to be consistently useful. Even in the cases where feasibility can be confirmed, we still need to obtain the new solution using the regular simplex feasibility conditions. Besides, the direct calculations associated with simultaneous changes given in Section 3.6.2 are straightforward and manageable.

To demonstrate the weakness of the rule, apply it to parts (a) and (b) of Problem 1 in this set. The rule fails to confirm the feasibility of the solution in (a) and does not apply in (b) because the changes in Di are outside the admissible ranges. Problem 13 further demonstrates this point.