In this work, we optimize the admission policy of application deployment requests submitted to data centers. Data centers are typically comprised of many physical servers. However, their resources are limited, and occasionally demand can be higher than what the system can handle, resulting with lost opportunities. Since different requests typically have different revenue margins and resource requirements, the decision whether to admit a deployment, made on time of submission, is not trivial. We use the Markov Decision Process (MDP) framework to model this problem, and draw upon the Approximate Dynamic Programming (ADP) paradigm to devise optimized admission policies. We resort to approximate methods because typical data centers are too large to solve by standard methods. We show that our algorithms achieve substantial revenue improvements, and they are scalable to large centers.