  We introduce the problem of finding a set $B$ of $k$ points in $[0,1]^n$ such
that the expected cost of the cheapest point in $B$ that dominates a random
point from $[0,1]^n$ is minimized. We study the case where the coordinates of
the random points are independently distributed and the cost function is
linear. This problem arises naturally in various application areas where
customers' requests are satisfied based on predefined products, each
corresponding to a subset of features. We show that the problem is NP-hard
already for $k=2$ when each coordinate is drawn from $\{0,1\}$, and obtain an
FPTAS for general fixed $k$ under mild assumptions on the distributions.
