  We report an apparatus and method capable of producing Bose-Einstein
condensates (BECs) of ~1x10^6 87Rb atoms, and ultimately designed for
sympathetic cooling of 133Cs and the creation of ultracold RbCs molecules. The
method combines several elements: i) the large recapture of a magnetic
quadrupole trap from a magneto-optical trap, ii) efficient forced RF
evaporation in such a magnetic trap, iii) the gain in phase-space density
obtained when loading the magnetically trapped atoms into a far red-detuned
optical dipole trap and iv) efficient evaporation to BEC within the dipole
trap. We demonstrate that the system is capable of sympathetically cooling the
|F=1,m_F=-1> and |1,0> sublevels with |1,+1> atoms. Finally we discuss the
applicability of the method to sympathetic cooling of 133Cs with 87Rb.
