This paper presents an analysis of the multi-stage Rankine cycle aiming at optimizing the power output from low-temperature heat sources such as geothermal or waste heat. A design methodology based on finite-time thermodynamics and the maximum power concept is used in which the shape and the power output of the maximum power cycle are identified and utilized to compare and evaluate different Rankine cycle configurations. The maximum power cycle provides the upper-limit power obtained from any thermodynamic cycle for specified boundary conditions and heat exchanger characteristics. It also provides a useful tool for studying power cycles and forms the basis for making design improvements.