We report on the optimal production of the Bose and Fermi mixtures with 87Rb and 40K in a crossed optical dipole trap (ODT). We measure the atomic number and lifetime of the mixtures in combination of the spin state |F = 9/2, m F = 9/2〉 of 40K and |1, 1〉 of 87Rb in the ODT, which is larger and longer compared with the combination of the spin state |9/2, 9/2〉 of 40K and |2, 2〉 of 87Rb in the ODT. We observe the atomic numbers of 87Rb and 40K shown in each stage of the sympathetic cooling process while gradually reducing the depth of the optical trap. By optimizing the relative loading time of atomic mixtures in the MOT, we obtain the large atomic number of 40K (∼6 × 106) or the mixtures of atoms with an equal number (∼1.6 × 106) at the end of evaporative cooling in the ODT. We experimentally investigate the evaporative cooling in an enlarged volume of the ODT via adding a third laser beam to the crossed ODT and found that more atoms (8 × 106) and higher degeneracy (T/T F = 0.25) of Fermi gases are obtained. The ultracold atomic gas mixtures pave the way to explore phenomena such as few-body collisions and the Bose–Fermi Hubbard model, as well as for creating ground-state molecules of 87Rb40K.