The performance of wireless sensor network applications is typically a function of the amount of data collected by the individual sensors and delivered to a set of sinks through multihop routing within the network. However, the energy-constrained nature of the nodes limits the operational lifetime of the network since energy is dissipated both in sensing and in communicating data across the network. There is thus an inherent trade-off in simultaneously maximizing the network lifetime and the application performance (characterized here by a network utility function). In this paper, we characterize this trade-off by considering a cross-layer design problem in a wireless sensor network with orthogonal link transmissions. We compute an optimal set of source rates, network flows, and radio resources at the transport, network, and radio resource layers respectively, while jointly maximizing the network utility and lifetime. Using dual decomposition techniques, we show that the cross-layer optimization problem decomposes vertically into three subproblems - a joint transport and routing problem, a radio resource allocation problem, and a network lifetime maximization problem, all of which interact through the dual prices for capacities of links and battery capacities of nodes.