The rapid growth of time-sensitive applications and services has driven enhancements to computing infrastructures. The main challenge that needs addressing for these applications is the optimal placement of the end-users demands to reduce the total power consumption and delay. One of the widely adopted paradigms to address such a challenge is fog computing. Placing fog units close to end-users at the edge of the network can help mitigate some of the latency and energy efficiency issues. Compared to the traditional hyperscale cloud data centres, fog computing units are constrained by computational power, hence, the capacity of fog units plays a critical role in meeting the stringent demands of the end-users due to intensive processing workloads. In this paper, we aim to optimize the placement of virtual machines (VMs) demands originating from end-users in a fog computing setting by formulating a Mixed Integer Linear Programming (MILP) model to minimize the total power consumption through the use of a federated architecture made up of multiple distributed fog cells. The obtained results show an increase in processing capacity in the fog layer and a reduction in the power consumption by up to 26% compared to the Non-Federated fogs network.