The emerging of the internet of things (IoT) led to increasing the computation resources required to satisfy a large number of requests from the connected devices, for this the Cloud Computing (CC) allows the processing of requests in the cloud to guarantee the efficiency of services for end-users. The main problem of the current CC architecture is the latency in real-time applications such as video streaming, which require a distributed architecture to support the future generation of applications. The Mobile Edge Computing (MEC) provides a fully distributed architecture where a part of processing executed in the edge of network which supports the requirements of IoT applications. In this paper, we propose to use the connected devices as on-demand virtual edge servers to provide computation services close to endusers where each submitted task is divided into a set of sub-tasks, each one can be executed by any other device which is a part of the virtual edge server according to the available resources in the selected device. In this context, we have formulated the partitioned and the offloading problem in MEC environment using linear programming techniques. Optimal Partitioned and Offloading (OPO) algorithm that allocates network, storage and computing resources to user application sub-tasks with respect to MEC constraints and user quality requirements is modeled, implemented, and evaluated. Results show the feasibility and efficiency of the proposed algorithms.