Question

. a) All steel manufactured by Steelco must meet the following requirements: 3.2-3.5 % carbon; 1.8-2.5% silicon; and 0.9-1.2 % nickel; and tensile strength of at least 45,000 per square inch (psi). Steelco manufactures steel by combining two alloys. The cost and properties of each alloy are given in the following Table. Alloy 1 $190 Alloy 2 $200 2.5 Cost per ton Percent silicon Percent nickel Percent carbon Tensile strength (psi) 2 1.5 1 3 50,000 42,000 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, has a tensile strength of 0.4(42,000) + 0.6(50,000). Formulate the problem of minimizing the cost of producing a ton of steel as an LP problem. (Please do not solve the actual problem) a one ton mixture consisting of 40% alloy 1 and 60% alloy 2

Answer 1

Let x % at alloy 1 and y % as alloy 2 is mixed then z = 190x/100 + 200y/100 z = 1.9x + 2y Constraints are 1.8 lessthanorequalto 2x/100 + 2.5 y/100 lessthanorequalto 2.5 0.9 lessthanorequalto x/100 + 1.5 y/100 lessthanorequalto 1.2 3.2 lessthanorequalto 3x/100 + 4y/100 lessthanorequalto 3.5 and 42000 x/100 + 50000 y/100 greaterthanorequalto 45000 0 lessthanorequalto x lessthanorequalto 100, 0 lessthanorequalto y lessthanorequalto 100 x + y = 100