In this paper we investigate the bandwidth (throughput) and energy efficiency considering both the physical layer and the medium access control (MAC) layer in multi-hop relay wireless networks. For a given distance between the source and the destination, as the number of relays increases the overhead necessary to operate the MAC protocol increases. However, the energy needed for a given throughput decreases when the distance between relays decreases. Thus there is an optimal number of relays that optimizes both the throughput and the energy efficiency. We analyze how the number of relays used between the source and the destination affects the throughput and the energy consumption. The energy-throughput relationship incorporating both the physical layer and the MAC layer was considered in the analysis and optimization of the number of relays. Based on the analysis we provide general criteria for the optimal number of relays.