In food processing, two-stage production systems with a batch processor in the first stage and packaging lines in the second stage are common and mostly separated by capacity- and time-constrained intermediate storage. This combination of constraints is common in practice, but the literature hardly pays any attention to this. In this paper, we show how various capacity and time constraints influence the performance of a specific two-stage system. We study the effects of several basic scheduling and sequencing rules in the presence of these constraints in order to learn the characteristics of systems like this. Contrary to the common sense in operations management, the LPT rule is able to maximize the total production volume per day. Furthermore, we show that adding one tank has considerable effects. Finally, we conclude that the optimal setup frequency for batches in the first stage is dictated by the storage time constraint.