Decisions about delivery programs to improve health status are characterized by indivisibilities or "lumpiness," interdependencies between case types with varying health output, high fixed costs, administrative constraints, and qualitative quity and political considerations. The nature of the constraints and the goal of health services strongly suggest a mathematical programming model to maximize a comprehensive measure of health status. In a previously unreported development, binary integer programming can be extended to consider shared fixed costs, a widespread problem in optimizing effectiveness measures such as health status. The model proposed here applies conceptually across all target populations and health programs and could be used to optimize the output of a total health system. The effects of such optimization would be appropriately reflected in the weighted life expectancy computed as a social indicator.