With the rapidly growing adoption of mobile devices, such as smartphones and tablets, the Internet multimedia traffic generated by mobile users has increased. An important problem involves providing users with satisfactory multimedia services. Multimedia cloud is emerging as a specific computing paradigm to resolve the aforementioned issue by providing quality of service (QoS) provisioning for multimedia services. Given the emergence of multimedia cloud services, studies of multi-platform multimedia information analysis are significantly supported. However, because the multimedia cloud includes limited resources, the allocation of resources to satisfy user requirements with respect to QoS guaranteed multimedia services is a challenging task. Additionally, the rapidly growing demand for multimedia services motivates cloud service providers (CSPs) to deploy a great number of servers in their data centers. However, the power consumption of the servers is a matter of increasing concern for CSPs. In this study, we investigate the problem of optimal resource allocation in a multimedia cloud by considering two server models, namely the constant-speed model and idle-speed model. Our objective involves achieving the tradeoff between response time and power consumption in the two server models. With respect to each server model, we formulate an optimization problem and solve it by employing the Lagrangian multiplier method. We present numerical results to verify the effectiveness of the proposed method. The numerical results indicate that our proposed resource allocation scheme achieves both minimal response time and power consumption when compared with the existing allocation schemes.