Steelco manufactures two types of steel (steel 1 and steel 2) at two locations (plants 1 and 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 2). Each plant has its own coal mine. Each day, 12 tons of coal are available at plant 1 and 15 tons at plant 2. Coal cannot be shipped between plants. 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 are 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 

Steelco manufactures two types of steel (steel 1 and steel 2) at two locations (plants 1 and 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 2). Each plant has its own coal mine. Each day, 12 tons of coal are available at plant 1 and 15 tons at plant 2. Coal cannot be shipped between plants. 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 are 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. Assuming that the only variable cost is the shipping cost, formulate and solve an LP to maximize Steelco’s revenues less shipping costs.

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TABLE 2 Resource Requirements for Steelco Iron Coal Blast Furnace Product Required Required Time Requested (1 Ton) (Tons) (Tons) (Hours) Steel 1 at plant 1 Steel 2 at plant 1 Steel 1 at plant 2 Steel 2 at plant 2 7 8695 5 32 3 2 1 1 1 1