This study is part of the "Grow More Food" campaign of our civilization for world peace and prosperity. It provides a working mathematical model for analyzing and optimizing the conjunctive use of surface and ground water resources of West Pakistan. In specific terms, the objective of the study is to determine the size of the canal system, the surface reservoir, and the ground water pumping facilities, such that, when the system is operated optimally, the capital and operation and maintenance costs of meeting the given irrigation water requirements are minimized. The results of this research indicate that by optimal conjunctive use management of the Indus Basin Irrigation System in Pakistan, the available water resources can be used more efficiently and at a lesser cost; the ground water aquifer can serve as a functional reservoir and a recycling facility, considerably increasing the usable water resources; and the present "use-when-available" supply system could be developed into a "supply-on-demand" system. This will make other technological, social, and economic inputs more effective and meaningful. As a result, the agricultural produce in the country could potentially be increased by 5 to 6 times. Continued research extension and development are necessary to explore this potential and determine its attainability. The scope of this study is limited to only a relatively small subset of the overall conjunctive use problem in West Pakistan. Some other problems, however, are identified and suggested for future research.