This paper shows that the power output of Various power plant configurations can be maximized by properly dividing the fixed inventory of heat exchange equipment among the heat transfer components of each plant. This conclusion is built over a sequence of fundamental power-maximization problems : the solar power plant with total area constraint, the solar power plant with storage by melting, the power plant with two heat exchangers and total area constraint, the combined-cycle power plant, the power plant viewed as an insulation between its heat source and heat sink. and the power plant with by-pass heat leak to the ambient. New diagrams are reported for the power plant at maximum power, and the refrigeration plant at maximum refrigeration load.