Blacktop Refining extracts minerals from ore mined at two different sites in Montana. Each ton of ore type 1 contains 20% copper, 20% zinc and 15% magnesium. Each ton of ore type 2 contains 30% copper, 25% zinc and 10% magnesium. Ore type 1 costs per ton and ore type 2 costs 0 per ton. Blacktop would like to buy enough ore to extract at least 8 tons of copper, 6 tons of zinc, and 5 tons of magnesium in the least costly manner. Find the optimal amount needed by Blacktop.
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