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Gogoma, Inc., has a two-stage production line. The first stage makes an engine and the second stage does the drone assembly. The engine stage has 30 parallel stations and the drone assembly consists 5 parallel stations. Because all engines are the same, the time for a station to build an engine is exactly 20 minutes. However, the drone customization processes make the drone assembly more difficult. Statistically, it takes 28 minutes on average to complete a drone assembly. To manage the inventory on engines, a Kanban system is utilized. In other words, the engine station cannot start to build a new engine until receiving a Kanban card. In the production system at Gogoma, there are m cards available (e.g., maximum inventory of engines is m). If Gogoma wants to be sure that the probability of a drone station finding an engine in stock is at least 90%, how large should m be?
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