von Liebigs law of the minimum is frequently proposed as a model of crop production which captures agronomic reality better than substitutional production functions. Whilst many studies of the law of the minimum and optimal fertilizer carryover have been undertaken separately, the law of the minimum for optimal fertilizer carryover has it would appear until now not been analysed, because of the non-differentiable nature of the agricultural producers objective function. In this paper I develop an optimal control model of fertilizer carryover subject to the law of the minimum using the differential inclusion approach to optimal control.