A fuzzy linear programming model (FLP) is formulated to derive optimal crop plans for an irrigation system with the aim of conjunctive utilization of water from surface reservoir and ground water aquifer, and demonstrated with a case study. The results of FLP model were compared with classical linear programming model (LP). The LP model model maximizes the net benefits from irrigation activities subject to various physical, economical, and water availability constraints. The fuzziness involved in the input variables such as inflows and ground water pumpage are considered in the FLP model. The FLP model maximizes the degree of satisfaction or truthness subject to object function, physical and economic constraints involving the fuzziness in the input variables. The increase in the degree of satisfaction or the truthness with increase in number of fuzzy variables was studied and the results are reported. It was found that the fuzziness in the ground water pumpage plays a prominent role in deriving the optimal operational strategies. From the optimal results it was found that the FLP model has resulted an optimal crop plan with a degree of truthness of 0.78 taking into account the fuzziness in different variables.