All steel manufactured by Steelton must meet the following requirements: 3.2-3.5

Question

All steel manufactured by Steelton 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). Steelton manufactures steel by combining two alloys. The cost and properties of each alloy are given in Table 47. 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.

Explanation / Answer

Decision variable:

Let X1 be the amount of alloy 1 used in steel

and X2 be the amount of alloy 2 used in steel

Objective Function:

Minimize Z = 190 X1+200 X2

Available Constraints:

1. Percent Silicon: 2 X1+ 2.5 X2 >= 1.8(X1+X2)

2. Percent Carbon = 3 X1+4X2 >=3.2 (X1+X2)

3. Percent Nickel =1 x1 + 1.5 x2 >= 0.9 (x1+x2)

4.Tensile Strength = 42000 (x1) +50000 (x2) >=45000

5. Non negative = X1 , X2 >= 0

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