This study considers a food production system that processes a single perishable raw material into several products having stochastic demands. In order to process an order, the amount of raw material delivery from storage needs to meet the raw material requirement of the order. However, the amount of raw material required to process an order is not exactly known beforehand as it becomes evident during processing. The problem is to determine the admission decisions for incoming orders so as to maximize the expected total revenue. It is demonstrated that the problem can be modeled as a single resource capacity control problem. The optimal policy is shown to be too complex for practical use. A heuristic approach is proposed which follows rather simple decision rules while providing good results. By means of a numerical study, the cases where it is critical to employ optimal policies are highlighted, the effectiveness of the heuristic approach is investigated, and the effects of the random resource requirements of orders are analyzed.