Open Radio Access Network (O-RAN) is very promising for flexible and efficient 5G and 6G wireless networks. The O-RAN architecture consists of three main units: Radio Unit (RU), Distributed Unit (DU), and Centralized Unit (CU). In this paper, we study the placement of virtualized DUs. This placement has strong consequences on cost and delay, among others, and is thus an important challenge. First, we analyze the throughput between the O-RAN interfaces. Based on our analysis, we propose an efficient Integer Linear Programming (ILP) model. The objective is to minimize the O-RAN cost depending on the DU placement while respecting the delay and capacity constraints. We evaluate our model on a real topology. Our results provide interesting insights into the cost savings with regard to a legacy architecture. Moreover, the proposed model provides solutions in a configuration where a fully centralized Cloud RAN architecture would not. We also estimate the limits of capacity of a given configuration.