This paper presents and evaluates the first open-source Network Function Virtualization (NFV)/Software Defined Networking (SDN)-based Mobile Edge Computing (MEC) platform. Our platform solves the Mobile Edge (ME) management issues with respect to Application (App) provisioning and traffic management. First, the ME Apps are managed as Virtual Network Functions (VNFs) on top of the virtual environment through the Juju VNF Manager (VNFM). Second, we develop an SDN controller to manage traffic on the ME System. Third, unlike other relevant architectures of ME systems, we use the control plane (i.e., S1 interface) to derive appropriate states for traffic management. Finally, we evaluate our solution in two use-cases: ME caching and Information Centric (ICN)/Delay Tolerant (DTN) Public Safety communication (PS). The MEC caching framework displays improved user Quality of Experience, e.g., latency, in comparison to direct communication, while the PS solution provides a residual mean of communication for rescue teams, when the network core (EPC) and a Public Data Network (PDN) are unavailable.