Modern data centres are increasingly adopting containers to enhance power and performance efficiency. These data centres consist of multiple heterogeneous machines, each equipped with varying amounts of resources such as CPU, I/O, memory, and network bandwidth. Data centers rent their resources to applications, which demand different amounts of resources and execute on machines for extended durations if the machines provide the demanded resources to the applications. Certain applications run efficiently on specific machines, referred to as system affinity between applications and machines. In contrast, others are incompatible with specific machines, referred to as anti-affinity between applications and machines. We consider that there are multiple applications, and data centers need to execute as many applications as possible. Data centers incur electricity based on CPU usage due to the execution of applications, with the cost being proportional to the cube of the total CPU usage. It is a challenging problem to place applications on the machines they have an affinity for while keeping the electricity cost in check. Our work addresses the placement problem of matching applications to machines to minimize overall electricity costs while maximizing the number of affinity pairs of machines and applications. We propose three solution approaches: (a) Power-Aware Placement (PAP): applications are placed on machines where power usage is minimized, (b) Affinity-Aware Placement (AAP): applications are placed on machines where affinity is maximized, (c) Combined Power-Affinity Placement (CPAAP): this approach integrates the benefits of both PAP and AAP. Our proposed approach improves the affinity satisfaction ratio by up to 4% while reducing the total system cost by up to 26% and improving the affinity payoff ratio by up to 37% compared to state-of-the-art approaches for real-life datasets.