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The government must manage public rangeland in the face of alternative multiple use interests, including wildlife and domestic livestock production. The objectives of this study were to estimate a production possibilities frontier for antelope (Antilocapra americana (Ord)) and stocker cattle on the Wyoming Red Desert and then evaluate the most economical combination for the specific production and price assumptions used in the analysis. Nine antelope-steer combinations were derived by using a linear programming model to maximize total number of animals subject to annual forage production on a representative 405-ha range site. The resulting 9 combinations included 72 head of antelope with no steers at one extreme and 35 head of stocker steers with no antelope at the other extreme, with various combinations of each in between. Because of the different forage preferences of antelope (primarily browse) and cattle (primarily grass), the marginal rates of substitution of cattle for antelope (MRS(c.a)) varied widely along the production possibilities frontier. Specifically, the MRS(c.a) was very low moving from 72 antelope-0 steers, to 69 antelope-29 steers, in terms of sacrificing only a few antelope (3) in exchange for a comparatively large number of steers (29). Conversely, the MRS(c.a.) moving from 69 antelope-29 steers, to 0 antelope-35 steers was very high in terms of sacrificing a relatively large number of antelope (69) in exchange for only a few additional steers (6). This wide range of substitution rates suggests that economic benefits from antelope and cattle would have to be extremely different before "multiple use" is not preferred in the case study setting.