In this paper, a model predictive control (MPC) policy is developed to simultaneously perform station keeping, attitude control, and momentum management of a nadir-pointing geostationary satellite equipped with three reaction wheels and four on-off electric thrusters mounted on two boom assemblies attached to the anti-nadir face of the satellite. The MPC policy includes an inner-loop SO(3)-based attitude control law to maintain a nadir-pointing attitude, and an outer loop for station keeping and momentum management. The MPC formulation makes use of two different prediction horizons; a short horizon is used for the states associated with the orbit's inclination and a longer horizon is used for all other states. This split-prediction horizon MPC policy leads to a significant reduction in delta-v compared to a single horizon. The continuous thrust command generated by the MPC policy is quantized as a single on-off pulse every feedback period in such a way that the predicted error in the states induced by quantization is minimized, which reduces the number of on-off pulses compared to other quantization approaches in the literature, including pulse-width modulation.