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The hybrid wireless-optical broadband-access network (WOBAN) is a promising architecture for access networks. Although the front-end wireless mesh networks in a WOBAN are self-healing, the back-end passive optical networks do not have survivability due to their tree topology. We propose a cost-effective protection method for WOBAN that deals with network element failures in the optical part of WOBAN. We define the maximum protection with minimum cost (MPMC) problem and show that the problem can be converted to the minimum cost maximum flow (MCMF) problem. We also present an integer linear programming (ILP) model for the MCMF problem. Numerical results are reported for the application of our algorithm to obtain the optimal solutions for different instances of the MPMC problem.