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STEELCO manufactures two types of steel (steel 1 and steel 2) at two locations (plant 1 and plant 2). Three resources are needed to manufacture a ton of steel: iron, coal, and blast furnace time. The two plants have different types of furnaces, so the resources needed to manufacture a ton of steel depend on the location (see Table below). Each plant has its own coal mine. Each day 12 tons of coal is available at plant 1 and 15 tons at plant 2. Each day, plant 1 has 10 hours of blast furnace time available, and plant 2 has 4 hours available. Iron ore is mined in a mine located midway between the two plants; 80 tons of iron is available each day. Each ton of steel 1 can be sold for $170/ton, and each ton of steel 2 can be sold for $160/ton. All steel that is sold is shipped to a single customer. It costs $80 to ship a ton of steel from plant 1, and $100 a ton from plant 2. BlueRail is a railway company which can ship coal between the two plants at $50/ton. However, BlueRail does not accept a job less than 6 tons. Steelco needs to maximise its profit. Please use linear programming (LP) to help Steelco decide whether to hire BlueRail or not. (10 marks)
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