Cloud computing is a powerful paradigm that can provide high-quality computation services to customers. Because its energy consumption has a large effect on its service price, this study investigates how to minimize the energy consumption while achieving adequate response times for requested computations. Such a problem is formulated as a nonlinear integer program. By deriving a state transition equation, this problem is transformed into an unconventional 0–1 knapsack problem, and dynamic programming is then used to solve it. In addition to this solution, we develop an energy-efficient job accommodation scheme that can manage dynamic jobs with varying frequencies throughout a day. Unlike existing studies that abruptly switch off old virtual machines and create new ones for upcoming jobs, this scheme tries to accommodate them with current virtual machines, and new virtual machines are not created unless necessary. Conversely, when the workload declines, jobs on energy-inefficient servers are moved to other servers, such that some energy-inefficient servers can be switched off to save energy. This scheme adjusts the computing power adaptively and smoothly without lowering the system’s quality of service. Experimental results demonstrate that the proposed solution outperforms a particle swarm optimizer and two other heuristics in terms of accommodating jobs and saving energy consumption.