In this article, we study the problem of assigning transmission ranges to the nodes of a wireless sensor network so as to minimize the global power consumption while ensuring a broadcast task. A first novelty is that our model takes into account both the transmission and the reception costs when evaluating the energy consumption. We establish a new analytical model and derive lower and upper bounds on region covering. Moreover, we show that the lower bound is asymptotically optimal and can be approached up to ε.