Most power plants are single purpose and produce only electric power. Others are dual-purpose plants since they not only generate electrical energy, but also produce fresh water through the desalination of seawater. The latter type is extensively used in countries where sources of fresh water are very scarce. This paper provides a detailed description of a dual system used in the Arabian Gulf region. In addition, it presents a mathematical optimization model for the process in which the operational cost is minimized for a specified time interval under several sets of constraints.