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Choosing an optimal placement of mesh points (MPs) to maximize the network throughput is one of the key concerns in building a wireless mesh network (WMN). The routing protocol used in the WMN, which governs the traffic distribution over the network, also affects the network throughput. Therefore, in this paper, we take account of the multi-path routing protocol used in a WMN in finding the optimal MP placement of the network such that the network throughput is maximized. Specifically, we formulate the routing results into a routing matrix and derive a formula to calculate the upper bound of the network throughput achieved by each wireless node in the network. We study some numerical examples under a WMN using different routing protocols such as hybrid wireless mesh protocol and routing information protocol. The results prove that the optimal MP placement can achieve almost twice of the other MP placements. Also, the MP placement affects both network maximum achievable throughput and the performance of routing protocols.