# 100% Rule

### From Glossary

This pertains to sensitivity analysis in linear programming. In its original form, it uses the convexity of the set of admissible changes
in the rim data to test whether a particular change is admissible: *any combination
of changes can occur as long as the total percentage deviation from
the coordinate extremes does not exceed* 100%. (Note: this
applies to right-hand sides (b) and costs (c) separately.)

More generally, suppose the optimal value remains constant if the cost coefficient vector in a linear program is replaced with any of (we could have and let be the j-th coordinate extreme for , but that is not necessary). Then, the optimal objective value is the same for , provided and

The same applies for convex combination of changes in the right-hand side (maybe with the origin, which is no change). If the objective value remains optimal at if is replaced with any of , then it is also optimal for the right-hand side so long that and