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Consider a plant whose output capacity depends on the amount of input as well as on the capacity of several machines that work in stages. Every now and then, these machines require maintenance, or else they'll break down. Taking a machine down for maintenance hurts the plants throughput, but so does a breakdown (and even more so). So the plant manager is left to decide which machines to maintain and when in order to achieve the highest possible throughput over the course of the planning horizon. In this video we model and solve this problem as a integer programming problem.