  Biological control, the use of predators and pathogens to control target
pests, is a promising alternative to chemical control. It is hypothesized that
the introduced predators efficacy can be boosted by providing them with an
additional food source. The current literature \cite{SP11} claims that if the
additional food is of sufficient constant quantity and quality then pest
eradication is possible in \emph{finite} time. The purpose of the current
manuscript is to show that to the contrary, pest eradication is \emph{not
possible} in finite time, for \emph{any} quantity and quality of constant
additional food. However for a density dependent quantity of additional food,
we show pest eradication in finite time is indeed possible. Our results have
large scale implications for the effective design of biological control methods
involving additional food.
