Overwintering of livestock has been regarded as a major problem in the Drakensberg grazing regions, which are characterized by high rainfall, cold winters and uneven topography. The latter limits arable land and this leads to mixed farming. The natural vegetation is predominantly sour veld; natural grazing becomes unpalatable and indigestible in winter. Farmers have for long handled this livestock overwintering problem by moving animals to grazing outside the region. The practice has been dying out. Linear programming was used to determine optimal livestock and cropping systems. The most profitable farming enterprise was shown to be dairying. Grazing and arable land should supply the dairy herd with its roughage needs and after these needs are satisfied, the remainder of arable land should be used for cash crops (maize and dry beans), leaving no room for either beer cattle or woolled sheep. If the farmer does not want to keep dairy cattle, his second best choice - with much lower profitability - is a combination of cash crops and woolled sheep. Sheep numbers have to be adjusted to the ability of natural grazing and crop residues to sustain their nutritional needs. It docs not pay to use arable land to produce feed or pastures for sheep. Beef cattle cannot compete economically with either dairy cattle, sheep or cash crops. Thus, the main problem in this region is not overwintering, but rather selection of optimal farming systems.