We propose a cloudlet network architecture to bring the computing resources from the centralized cloud to the edge. Thus, each User Equipment (UE) can communicate with its Avatar, a software clone located in a cloudlet, and can thus lower the end-to-end (E2E) delay. However, UEs are moving over time, and so the low E2E delay may not be maintained if UEs' Avatars stay in their original cloudlets. Thus, live Avatar migration (i.e., migrating a UE's Avatar to a suitable cloudlet based on the UE's location) is enabled to maintain the low E2E delay between each UE and its Avatar. On the other hand, the migration itself incurs extra overheads in terms of resources of the Avatar, which compromise the performance of applications running in the Avatar. By considering the gain (i.e., the E2E delay reduction) and the cost (i.e., the migration overheads) of the live Avatar migration, we propose a PRofIt Maximization Avatar pLacement (PRIMAL) strategy for the cloudlet network in order to optimize the tradeoff between the migration gain and the migration cost by selectively migrating the Avatars to their optimal locations. Simulation results demonstrate that as compared to the other two strategies (i.e., Follow Me Avatar and Static), PRIMAL maximizes the profit in terms of maintaining the low average E2E delay between UEs and their Avatars and minimizing the migration cost simultaneously.