The Internet of Everything (IoE) has been greatly empowered by the technical standards introduced in the 5G evolution of cellular systems. While 5G allows for IoE communication, the realization of a network in which self-sustaining machines can observe, sense, and actuate their environment has yet to be implemented. Future wireless networks, such as 6G and beyond, are expected to enable integrated Sensing and Communication (ISAC) through the shared use of a single hardware platform and a joint signal processing framework. In this context, dual-function radar communication systems (DFRC) have emerged as a promising ISAC technology for providing sensing capabilities in pre-deployed wireless communication networks. This work employs a multi-user, multi-target DFRC system with a full-duplex base station (FD-BS) for communication and sensing. We aim to minimize the total power usage at the FD-BS while meeting desired communication and sensing requirements. As the formulated problem is non-convex, we use semi-definite relaxation and generalized Rayleigh quotient-based optimization techniques to design the jointly optimal radar signal, transmit beamforming vectors, and receive combiners. Simulation results demonstrate that the proposed algorithm yields a fast-converging near-optimal solution, outperforming existing benchmarks for different values of key system parameters.