In modern Open RAN architectures, the classic gNB radio protocol stack is disaggregated and implemented in different virtualized components, the Centralized Unit (CU), the Distributed Unit (DU), and the Radio Unit (RU). Each of these units is deployed throughout the cloud-enabled RAN infrastructure in order to achieve users' required Quality of Service (QoS). Within this framework, our study is dedicated to maximizing the admission of User Equipments (UEs) into the system while ensuring their specific QoS needs. We focus on two primary tasks: (i) establishing an association between UEs and RUs and (ii) placing CUs and DUs across the network's cloud hosts. We initially address these tasks by formulating the joint association-placement optimization problem, subject to the system's available resources and QoS-related constraints. Although it is an NP-Hard problem, we discuss how we can frame it into an Integer Linear Programming (ILP) model. Then, we propose an approximation algorithm based on the decomposition of the original ILP model. We show through exhaustive simulations that our proposed ILP model provides higher admissibility levels than other baseline models. Moreover, it significantly minimizes the deployment costs and increases the overall fairness. Finally, we remark that our decomposition algorithm presents a short optimality gap in practice, with up to 6% less admissions, while reducing the solution time by up to 98%.