Wireless powered communication (WPC), where the required energy for communication is obtained via radio frequency (RF) energy harvesting, is a promising technology for the upcoming self-sustainable Internet of Things (IoT) networks. In this paper, a multiuser IoT network is considered, where an energy-constrained relay assists the information transmission of a number of IoT devices to the access point (AP) using WPC. In particular, the relay acquires the energy needed for information forwarding from the RF energy transfer of the AP, which serves as a dedicated energy transmitter for the relay. The objective is to maximize the total network throughput by jointly optimizing the wireless energy transfer (WET) duration and the relay's energy expenditure in each time slot, subject to the energy causality constraint, for both amplify-and-forward (AF) and decode-and-forward (DF) relaying protocols. We show that the optimization problems for both the AF- and DF-based systems are convex and thus can be solved using convex optimization techniques. Our analysis shows that the solution of the sum-throughput maximization problems depends on the scheduling order of the IoT devices and the optimal solution is derived for different ordering scenarios. Finally, numerical simulations are presented to corroborate our analysis.