This paper addresses the problem of determining the optimal mix of energy conservation, passive solar, and zone heating systems in residential buildings. Analytic solutions to constrained and global optimization problems are presented. This work draws upon the Lagrangian multiplier technique used in related studies of energy conservation and passive solar design. Graphs are presented showing the optimal cost fractions for energy conservation, passive solar, and a zone heater as a function of the initial cost constraint, for a reference building in Dodge City, Kansas. The use of a zone heater is shown to reduce the annual energy requirements for space heating, and increase the life cycle savings. Also presented are design curves for the required zone heater capacity as a function of the thermal time constant for a given zone, heater response time, and interzonal heat transfer. Finally, design curves for the zone mean radiant temperature as a function of zone size, zone heater temperature, zone heater area, and interzonal heat transfer are presented.

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