We investigate the problem of energy-efficient broadcast routing over stationary wireless adhoc networks where the host is not mobile. We define the lifetime of a network as the duration of time from the network initialization until the first node failure due to the battery exhaustion. We provide a globally optimal solution to the problem of maximizing a static network lifetime through a graph theoretic approach. We make use of this solution to develop a periodic tree update strategy for dynamic load balancing and show that a significant gain in network lifetime can be achieved. We also provide extensive comparative simulation studies on parameters that affect the lifetime of a network.