This paper considers a network of a multi-antenna array base station (BS) and a reconfigurable intelligent surface (RIS) to deliver both information to information users (IUs) and power to energy users (EUs). The RIS links the connection between the IUs and the BS as there is no direct path between the former and the latter. The EUs are located nearby the BS in order to effectively harvest energy from the high-power signal from the BS, while the much weaker signal reflected from the RIS hardly contributes to the EUs' harvested energy. To provide reliable links for all users over the same time-slot, we adopt the transmit time-switching (transmit-TS) approach, under which information and energy are delivered over different time-slot fractions. This allows us to rely on conjugate beamforming for energy links and zero-forcing/regularized zero-forcing beamforming (ZFB/RZFB) and on the programmable reflecting coefficients (PRCs) of the RIS for information links. We show that ZFB/RZFB and PRCs can be still separately optimized in their joint design, where PRC optimization is based on iterative closed-form expressions. We then develop a path-following algorithm for solving our max-min IU throughput optimization problem subject to a realistic constraint on the quality-of-energy-service in terms of the EUs' harvested energy thresholds. We also propose a new RZFB for substantially improving the IUs' throughput.