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This paper studies a novel wireless powered Internet of Things (IoT) network that consists of (a) a Hybrid Access Point (HAP) that charges devices and also helps facilitate backscattering transmissions, (b) devices that use active Radio Frequency (RF) and backscattering transmissions, and (c) a mobile data collector. Our aim is to maximize the amount of data received by the HAP and data collector. The main problem is to determine the charging duration of the HAP and link activation schedule of devices. We formulate a novel Mixed Integer Linear Program (MILP) and also propose a heuristic algorithm named Reduced-Set Linear Program Approximation (RS-LPA). The results show that (i) throughput increases with the number of backscatter transmission sets, (ii) smaller amount of data is uploaded to the mobile collector when sampling cost is low, and (iii) the throughput of RS-LPA is on average 10.55% lower than MILP.