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In the era of pervasive digital connectivity, intelligent surveillance systems (ISS) have become essential tools for ensuring public safety, protecting critical infrastructure, and deterring security threats in various environments. The current state of these systems heavily relies on the computational capabilities of mobile devices for tasks such as real-time video analysis, object detection, and tracking. However, the limited processing power and energy constraints of these devices hinder their ability to perform these tasks efficiently and effectively. The dynamic nature of the surveillance environment also adds complexity to the task-offloading process. To address this issue, mobile edge computing (MEC) comes into play by offering edge servers with higher computational capabilities and proximity to mobile devices. It enables ISS by offloading computationally intensive tasks from resource-constrained mobile devices to nearby MEC servers. Therefore, in this paper, we propose and implement an energy-efficient and cost-effective task-offloading framework in the MEC environment. The amalgamation of binary and partial task-offloading strategies is used to achieve a cost-effective and energy-efficient system. We also compare the proposed framework in MEC with mobile cloud computing (MCC) environments. The proposed framework addresses the challenge of achieving energy-efficient and cost-effective solutions in the context of MEC for ISS. The iFogSim simulator is used for implementation and simulation purposes. The simulation results show that the proposed framework reduces latency, cost, execution time, network usage, and energy consumption.