We report the production of a high phase-space density mixture of $^{87}$Rb and $^{133}$Cs atoms in a levitated crossed optical dipole trap as the first step towards the creation of ultracold RbCs molecules via magneto-association. We present a simple and robust experimental setup designed for the sympathetic cooling of $^{133}$Cs via interspecies elastic collisions with $^{87}$Rb. Working with the $|F=1, m_F=+1 >$ and the $|3, +3 >$ states of $^{87}$Rb and $^{133}$Cs respectively, we measure a high interspecies three-body inelastic collision rate $sim 10^{-25}-10^{-26} rm{cm}^{6}rm{s}^{-1}$ which hinders the sympathetic cooling. Nevertheless by careful tailoring of the evaporation we can produce phase-space densities near quantum degeneracy for both species simultaneously. In addition we report the observation of an interspecies Feshbach resonance at 181.7(5) G and demonstrate the creation of Cs$_{2}$ molecules via magneto-association on the 4g(4) resonance at 19.8 G. These results represent important steps towards the creation of ultracold RbCs molecules in our apparatus.
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