Abstract-In this work, we study the problem of allocating resources in a multi-service cellular network aiming at maximizing the total system rate while providing suitable Quality of Experience (QoE) to the network users. In our formulation, we try to satisfy at least a certain number of users per service plan, which is an important constraint from the mobile network operators' perspective. We manage to reformulate this nonlinear optimization problem as an Integer Linear Problem (ILP), that can be solved by standard methods. However, due to the exponentially high complexity to solve large instances of this problem, we propose and evaluate a suboptimal algorithm with a much lower complexity, called Rate Maximization under Experience Constraints (RMEC), whose main idea is to divide the problem into three smaller subproblems with reduced complexity. By means of computational simulations, we show that our proposed algorithm presents a near optimal performance and outperforms the state-of-art solution of the literature.