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\begin{document}
\title{Exercise for Optimal control -- Week 2\date{}}
\author{Choose \textbf{one }problem to solve.}
\maketitle
\begin{xca}[Insect control]
Let $w(t)$ and $r(t)$ denote, respectively, the worker and reproductive
population levels in a colony of insects, e.g. wasps. At any time
$t$, $0\le t\le T$ in the season the colony can devote a fraction
$u(t)$ of its effort to enlarging the worker force and the remaining
fraction $u(t)$ to producing reproductives. The per capita mortality
rate of workers is $\mu$ and the per capita natality rate is $b$
when full effort is put on the worker population. Assume $\mu