The design of a wireless network is often critically affected by issues such as determining the optimal density of Access Points (APs) and the optimal channel assignment by exploiting partially overlapped channels (POCs) for significantly improving the network performance in terms of maximizing the overall network capacity. Contemporary research works have traditionally dealt with these two problems in an isolated manner though they should be considered within the same problem formulation. Furthermore, even though deployment of additional APs can improve the network capacity in case there are a few APs in a given area, the APs cannot be indefinitely added to the wireless network. This means that there is an upper bound to the network capacity maximization with respect to the number of APs. In fact, the network capacity starts to dramatically decrease when the number of deployed APs becomes excessive. This performance decrease can be accredited to the substantial interference among the high number of deployed APs. In order to address this challenge, in this paper, we propose an approach to jointly optimize the number of APs and POCs assignment. Our proposal derives the existence of the optimal density of APs with POCs, and models the POC assignment to the deployed APs from a novel perspective. Computer-based simulations are conducted to demonstrate the effectiveness of our proposal.