Wireless charging coupled with computation offloading in edge networks offers a promising solution for realizing power-hungry and computation intensive applications on user devices. We consider a mutil-access edge computing (MEC) system with collocated MEC servers and base-stations/access points (BS/AP) supporting multiple users requesting data computation and wireless charging. We propose an integrated solution with computation offloading to satisfy the largest proportion of requested wireless charging while keeping the energy consumption at the minimum subject to the MEC-AP transmit power and latency constraints. We propose a novel algorithm to perform data partitioning, time allocation, transmit power control and design the optimal energy beamforming for wireless charging. Our resource allocation scheme offers an energy minimizing solution compared to other schemes while also delivering higher amount of transferred charge to the users.