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The proliferation of innovative mobile services such as augmented reality, networked gaming, and autonomous driving has spurred a growing need for low-latency access to computing resources that cannot be met solely by existing centralized cloud systems. Mobile Edge Computing (MEC) is expected to be an effective solution to meet the demand for low-latency services by enabling the execution of computing tasks at the network-periphery, in proximity to end-users. While a number of recent studies have addressed the problem of determining the execution of service tasks and the routing of user requests to corresponding edge servers, the focus has primarily been on the efficient utilization of computing resources, neglecting the fact that non-trivial amounts of data need to be stored to enable service execution, and that many emerging services exhibit asymmetric bandwidth requirements. To fill this gap, we study the joint optimization of service placement and request routing in MEC-enabled multi-cell networks with multidimensional (storage-computation-communication) constraints. We show that this problem generalizes several problems in literature and propose an algorithm that achieves close-to-optimal performance using randomized rounding. Evaluation results demonstrate that our approach can effectively utilize the available resources to maximize the number of requests served by low-latency edge cloud servers.