  We prove a hydrodynamic limit for the totally asymmetric simple exclusion
process with spatially inhomogeneous jump rates given by a speed function that
may admit discontinuities. The limiting density profiles are described with a
variational formula. This formula enables us to compute explicit density
profiles even though we have no information about the invariant distributions
of the process. In the case of a two-phase flow for which a suitable p.d.e.
theory has been developed we also observe that the limit profiles are entropy
solutions of the corresponding scalar conservation law with a discontinuous
speed function.
