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It is a challenging task for multi-hop wireless networks to support multimedia applications with quality-of service (QoS) requirements. This letter presents a joint cross layer optimization approach, i.e., joint medium access control, routing, and energy distribution. User satisfaction represented by user utility is maximized within the required network lifetime, given the constraints on the total available energy in the network and the minimum user rates. Although the resulting optimization problem is nonlinear and nonconvex, we prove that it is approximately equivalent to a two-step convex problem. Furthermore, we prove that the problem of maximizing network utility within achievable network lifetime is quasiconvex.