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The report discusses the theory of demand for irrigation water and includes an empirical application of linear programming to the estimates of irrigation water demand on the Jordan River Basin of Utah. Water diverted for irrigation is valued at a maximum of approximately $14 an acre foot. Consumptively used, it has a maximum value of over $36. Supply functions for irrigation and M and I water were estimated subject to constraints on wetland diversions and basin outflow from the Jordan Basin. Estimated costs of supplying M and I water varies from $70 to over $236 per acre-foot, and the cost of supplying irrigation water varies from $.52 to over $112 per acre-foot. An optimizing model of water resources allocation was developed by comparing the supply and demand models into a single linear programming problem (a graphical solution is also presented).