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 crop-reporting district. 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. Quantities demanded by beef cows for each of the three co-products considered, sugarbeet pulp, wheat middlings, and potato waste, are large relative to other species because of their predominance in the district. At the current price for sugarbeet pulp, quantity demanded by district livestock is low. However quantity demanded is price elastic and becomes much greater at lower prices. Wheat middlings can be an important component of livestock rations, even at higher prices. At a price slightly below the current price, local livestock demand would exhaust the wheat middlings produced at the district's only wheat processing plant. Potato waste is most appropriate for ruminant diets because these animals are able to consume a large quantity of this high moisture feedstuff. Potato waste can be a cost-effective component in beef and dairy rations. Practically, livestock markets for potato waste must be in close proximity to a potato processing plant. Its high moisture content limits the distance it can be economically transported. At current prices, potato waste can be economically included in the ration for beef cows on a farm nearly 100 miles from the processing plant, although storage challenges may restrict use of the feed to closer operations.