We report the first realization of a quantum degenerate mixture of bosonic $^{87}$Rb and fermionic $^{171}$Yb atoms in a hybrid optical dipole trap with a tunable, species-dependent trapping potential. $^{87}$Rb is shown to be a viable refrigerant fo
r the non-interacting $^{171}$Yb atoms, cooling up to $2.4 times 10^5$ $^{171}$Yb atoms to a temperature of $T/T_F = 0.16(2) $ while simultaneously forming a $^{87}$Rb BEC of $3.5 times 10^5$ atoms. Furthermore we demonstrate our ability to independently tailor the potentials for each species, which paves the way for studying impurities immersed in a Bose gas.
