Co-products of processing agricultural commodities are often marketed through private transaction rather than through public markets or those in which public transaction information is recorded or available. The resulting lack of historical price information prohibits the use of positive time series techniques to estimate demand. Demand estimates for co-products are of value to both livestock producers, who obtain them for use in livestock rations, and processors, who must sell or otherwise dispose of them. Linear programming has long been used, first by researchers and later as a mainstream tool for nutritionists and producers, to formulate least cost livestock rations. Here it is used as a normative technique to estimate step function demand schedules for co-products by individual livestock classes within a region. Regression is then used to smooth step function demand schedules by fitting demand data to generalized Leontief cost functions. Seemingly unrelated regression is used to estimate factor demand first adjusted for data censoring using probit analysis. Demand by individual livestock classes is aggregated over the number of livestock within a region. Species important to demand for each co-product are identified and own price elasticity for individual livestock classes and all livestock are estimated.