  Initially announced by Dorfman in 1943, (Binomial) Group Testing (BGT) was
quickly recognized as a useful tool in many other fields as well. To apply any
particular BGT procedure effectively, one first of all needs to know an
important operating characteristic, the so called Optimal Cut-Point (OCP),
describing the limits of its applicability. The determination of the latter is
often a complicated task. In this work, we provide a generic algorithm suitable
for a wide class of the BGT procedures and demonstrate its applicability by
example. The way we do it exhibits independent interest since we link the BGT
to seemingly unrelated field -- the bifurcation theory.
