The paper describes a special case of a base station placement in wireless network with linear topology. Each station is equipped with access point (for example IEEE 802.11) that is used by the objects to send their data via the network, and with a relay equipment that allows the station to connect to the neighboring stations. Each station is described by the coverage radius and the communication radius to other stations. The goal is to determine such placement of the stations which will maximize the total coverage on the linear section by the given set of stations. Two formal problem statements are described and analyzed: the statement in the extremal combinatorial form and the formulation of the problem as a mixed-integer linear programming model. The main result is the development of a special branch and bound algorithm for solving the problem represented in the combinatorial form. The results of a comparative computational experiment by three approaches: by the brute force method, by the branch and bound algorithm and solving the problem in the form of the mixed-integer linear programming are given.