The U.S. Department of Energy and Idaho National Laboratory are developing a very high temperature reactor to serve as a demonstration of state-of-the-art nuclear technology. The purpose of the demonstration is twofold: (a) efficient, low-cost energy generation and (b) hydrogen production. Although a next-generation plant could be developed as a single-purpose facility, early designs are expected to be dual purpose, as assumed here. A dual-purpose design with a combined cycle of a Brayton top cycle and a bottom Rankine cycle was investigated. An intermediate heat transport loop for transporting heat to a hydrogen production plant was used. Helium, CO2, and a helium-nitrogen mixture were studied to determine the best working fluid in terms of the cycle efficiency. The relative component sizes were estimated for the different working fluids to provide an indication of the relative capital costs. The relative size of the turbomachinery was measured by comparing the power input/output of the component. For heat exchangers the volume was computed and compared. Parametric studies away from the baseline values of the cycle were performed to determine the effects of varying conditions in the cycle. This gives some insight into the sensitivity of the cycle to various operating conditions as well as trade-offs between efficiency and component size. Parametric studies were carried out on reactor outlet temperature, mass flow, pressure, and turbine cooling.