In this paper, we consider the problem of obtaining the optimal parameters for a wirelessly powered backscatter communication network. It is assumed that one user scatters the signal transmitted from the power station while the other one employes energy harvesting to power its data transmission. Both users transmit their data to the receiver by adopting time-division multiple access technique. The optimal backscatter, transmission and energy harvesting periods that maximize the overall transmitted data in a given time interval are determined using results from recent literature on the subject. The solution is employed to obtain the performance results for FM, TV and WiFi signals which constitute the three main RF sources used in practice.