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In this paper, we study the problem of supporting multicast traffic in wireless sensor networks with network coding. On one hand, coding operations can reduce power consumption and consequently improve the network lifetime. On the other hand, performing network coding requires the use of the limited resources of the sensor nodes such as memory and energy. We study the tradeoff between maximizing the network lifetime and minimizing the number of network coding operations. We introduce the coding flow variables which enable us to determine the rate at which different operations (e.g., forwarding, replication, and coding) are performed in each sensor node. Using the coding flow variables, we formulate the maximum-lifetime minimum-resource (MLMR) coding subgraph problem as a linear programming problem. The objective in MLMR problem is to jointly maximize the network lifetime and minimize the rate of performing network coding. We propose an MLMR algorithm in order to obtain the optimal coding subgraph. We investigate the lifetime-resource tradeoff assuming that the cost of performing network coding varies for intermediate nodes. Simulation results show that the network lifetime can considerably be improved when the cost of performing network coding is relatively low compared to the case that this cost is high for intermediate nodes in the network. Moreover, results show that the network lifetime can substantially be increased using MLMR algorithm compared with the classical multicast with Steiner tree and another algorithm which uses network coding without considering the broadcast nature of wireless links.