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Hybrid WLAN mesh networks use a combination of nodes that are continuously powered and those that are powered using an energy sustainable source such as solar power. In this paper we consider the problem of cost-optimal placement of the energy sustainable nodes in these types of hybrid networks. We first introduce a cost model that takes into account the provisioning required to operate the solar/wind powered nodes subject to a desired node outage criterion. We then formulate the design problem as a Mixed Integer Quadratic Problem (MIQP). A branch and bound approach is used to obtain node positioning solutions and is compared with a proposed algorithm that uses optimum shortest path routes. Our results show that there is a significant improvement in cost that can be obtained using the proposed methodology and that the branch and bound approach achieves the optimum assignment for a variety of network examples.