Reducing the total power consumption and network delay are among the most interesting issues facing large-scale Mobile Cloud Computing (MCC) systems and their ability to satisfy the Service Level Agreement (SLA). Such systems utilize cloud computing infrastructure to support offloading some of user's computationally heavy tasks to the cloud's datacenters. However, the delay incurred by such offloading process lead the use of servers (called cloudlets) placed in the physical proximity of the users, creating what is known as Mobile Edge Computing (MEC). The cloudlet-based infrastructure has its challenges such as the limited capabilities of the cloudlet system (in terms of the ability to serve different request types from users in vast geographical regions). To cover the users demand for different types of services and in vast geographical regions, cloudlets cooperate among each other by passing user requests from one cloudlet to another. This cooperation affects both power consumption and delay. In this work, we present a mixed integer linear programming (MILP) optimization model for MEC systems with these two issues in mind. Specifically, we consider two types of cloudlets: local cloudlets and global cloudlets, which have higher capabilities. A user connects to a local cloudlet and sends all of its traffics to it. If the local cloudlet cannot serve the desired request, then the request is moved to another local cloudlet. If no local cloudlet can serve the request, then it is moved to a global cloudlet which can serve all service types. The process of routing requests through the hierarchical network of cloudlets increases power consumption and delay. Our model minimizes power consumption while incurring an acceptable amount of delay. We evaluate it under several realistic scenarios to show that it can indeed be used for power optimization of large-scale MEC systems without violating delay constraints.