Energy-related costs have become one of the major economic factors in IT data-centers, and companies and the research community are currently working on new efficient power-aware resource management strategies, also known as “Green IT”. Here we propose a framework for autonomic scheduling of tasks and web-services on cloud environments, optimizing the profit taking into account revenue for task execution minus penalties for service-level agreement violations, minus power consumption cost. The principal contribution is the combination of consolidation and virtualization technologies, mathematical optimization methods, and machine learning techniques. The data-center infrastructure, tasks to execute, and desired profit are cast as a mathematical programming model, which can then be solved in a different ways to find good task schedulings. We use an exact solver based on mixed linear programming as a proof of concept but, since it is an NP-complete problem, we show that approximate solvers provide valid alternatives for finding approximately optimal schedules. The machine learning is used to estimate the initially unknown parameters of the mathematical model. In particular, we need to predict a priori resource usage (such as CPU consumption) by different tasks under current workloads, and estimate task service-level-agreement (such as response time) given workload features, host characteristics, and contention among tasks in the same host. Experiments show that machine learning algorithms can predict system behavior with acceptable accuracy, and that their combination with the exact or approximate schedulers manages to allocate tasks to hosts striking a balance between revenue for executed tasks, quality of service, and power consumption.