Multi-access Edge Computing (MEC) is a new network architecture that allows applications and network services to be executed at the edge of the network. This is done by running these services on commodity servers that are placed in close proximity to the network edge and to the cellular base stations in wireless networks. This architecture provides high bandwidth and low latency for network functions and other applications. However, the availability of the resources at the network edge is limited and thus one of the main challenges in deploying this new paradigm is the ability to locate these latency sensitive services in the appropriate network location according to the specific demand for each service and the relevant latency constraints. In this paper we address this challenge by defining the Virtual Network Functions Placement and Assignment Problem (VNFPAP) and providing algorithms with guaranteed performance for it. We also show by simulating our algorithms on real mobile data that in realistic scenarios they perform much better than current used heuristics.