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IEEE 802.16j is a wireless broadband networking standard that integrates infrastructure base stations with multihop relay technology. Relay stations can provide substantial gains of coverage area and capacity of the cell compared to a base station alone. In this paper, we introduce an optimization problem of cost-effective relay station deployment for the IEEE 802.16j networks in the case of extending the coverage on the new residential area. First, the coverage area, which is defined as an area where the user has a signal- to-noise value greater than a given threshold value, is calculated. After that, the number of relay stations and their optimal positions which maximize the provider's profit are found, taking into account one-time costs, such as CAPEX and IMPEX, as well as recurring costs, like OPEX. The proposed relay deployment mechanism allows the providers to maximize their own profit if they want to extend the coverage area to attract new customers.