In wireless ad hoc networks (WANETs), e.g. wireless sensor networks, battery-powered devices are constrained by limited amount of energy. Many WANET applications require that the duration (called lifetime) for which the network remains operational - until the first node exhausts its battery energy is maximized. We study the problem of maximizing the lifetime of WANET broadcast trees under two receiver cost models: 1) the constant receiver power (CORP) model, in which a receiver consumes a fixed amount of energy for receiving an information bit; and, 2) the transmitter-receiver power tradeoff (TREPT) model, in which the amount of energy consumed by a receiver is a function of the received signal power and hence the transmitter power. We propose a graph theoretic solution for CORP model to find a maximum lifetime tree and a binary search based solution for TREPT model to determine power assignment which maximizes the lifetime of a given broadcast tree. Both polynomialtime solutions are formally proved to be optimal.