  This paper is concerned with the spatially periodic Fisher-KPP equation
$u_t=(d(x)u_x)_x+(r(x)-u)u$, $x\in \mathbb{R}$, where $d(x)$ and $r(x)$ are
periodic functions with period $L>0$. We assume that $r(x)$ has positive mean
and $d(x)>0$. It is known that there exists a positive number $c^*_d(r)$,
called the minimal wave speed, such that a periodic traveling wave solution
with average speed $c$ exists if and only if $c \geq c^*_d(r)$. In the
one-dimensional case, the minimal speed $c^*_d(r)$ coincides with the
``spreading speed'', that is, the asymptotic speed of the propagating front of
a solution with compactly supported initial data. In this paper, we study the
minimizing problem for the minimal speed $c^*_d(r)$ by varying $r(x)$ under a
certain constraint, while $d(x)$ arbitrarily. We have been able to obtain an
explicit form of the minimizing function $r(x)$. Our result provides the first
calculable example of the minimal speed for spatially periodic Fisher-KPP
equations as far as the author knows.
