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.