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Charm City Mining Company owns two mines, each of which produces three grades of ore- high, medium, and low. The company has a contract to supply a smelting company with at least 8 tons of high-grade ore, 10 tons of medium-grade ore, and 18 tons of low-grade ore. Each mine produces a certain amount of each type of ore during each hour that it operates. Mine 1 produces 5 tons of high-grade ore, 3 tons of medium-grade ore, and 3.5 tons of low grade ore per hour. Mine 2 produces 2.2, 2.5, and 10.2 tons, respectively, of high-, medium-, and low-grade ore per hour. It costs Charm City $300 per hour to mine each ton of ore from mine 1, and it costs $250 per hour to mine each ton of ore from mine 2. The company wants to determine the number of hours it needs to operate each mine so that its contractual obligations can be met at the lowest cost.
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