This paper deals with the problem of determining the optimum combination of sheep and beef cattle on grazing properties. A major difficulty is that iso-cost functions (production possibility curves) for sheep and cattle are unstable and difficult to estimate because of sheep-cattle-pasture interaction. After discussion of theoretical difficulties consideration is given to practical approaches, based on the iso-cost function concept, which might provide graziers with useful guide-lines. Evidence is presented which suggests that the substitution rate between sheep and cattle with respect to pasture is not constant, and probably varies with stocking rate.