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This analysis was conducted to aid management of a large corporation's Research and Engineering Division in planning the allocation of its budget among six areas of responsibility. The allocation problem is complicated by multiple competing objectives and by uncertainty in the outcome corresponding to a given allocation policy. These characteristics were taken into account by eliciting a multiattribute utility function from two directors to quantify their preferences for multidimensional uncertain outcomes. Independence conditions verified with the two directors permitted decomposition of this function into appropriately scaled sums and products of one-dimensional utility functions, and this greatly simplified th assessment task. The expectation of the multiattribute utility function was used as the objective function to be maximized in the analytical model developed. The directors' judgments concerning the relationships between the allocation variables and the outcomes were quantified by assessing subjective probability distributions at fixed values of the allocation variables.