Dual source systems can request the necessary power supply from two different power sources, with specific operational characteristics and requirements. Exploiting the corresponding combination possibilities opens new optimization potentialities for several practical applications, as in the case of hybrid vehicles. This paper discusses the optimization strategy to be followed to obtain an absolute minimum for the case of an integral equality constraint on one of the two sources and a fixed time horizon. It derives analytically an algorithm, whose optimality is confirmed by comparisons with the results of extensive numerical optimizations.