# Mathematics

All steel manufactured by Steelco must meet the following requirements: 3.2–3.5% carbon; 1.8–2.5% silicon; 0.9–1.2% nickel; tensile strength of at least 45,000 pounds per square inch (psi). Steelco manufactures steel by combining two alloys. The cost and properties of each alloy are given in Table.

 Alloy 1 Alloy 2 Cost per ton (\$) \$190 \$200 Percent silicon 2 2.5 Percent nickel 1 1.5 Percent carbon 3 4 Tensile strength (psi) 42,000 50,000

Assume that the tensile strength of a mixture of the two alloys can be determined by averaging that of the alloys that are mixed together. For example, a one-ton mixture that is 40% alloy 1 and 60% alloy 2 has a tensile strength of 0.4(42,000) + 0.6(50,000).

Use linear programming to determine how to minimize the cost of producing a ton of steel.

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