  Given a compact Riemannian manifold with density $M$ without boundary and the
real line $\mathbb{R}$ with constant density, we prove that isoperimetric
regions of large volume in $M\times\mathbb{R}$ with the product density are
slabs of the form $M\times [a,b]$. We previously prove, as a necessary step,
the existence of isoperimetric regions in any manifold of density where a
subgroup of the group of transformations preserving weighted perimeter and
volume acts cocompactly.
