Suppose a specialty steel company receives an order for 200 tons of steel containing at least 3 percent nickel and 2 percent manganese, with a carbon content not exceeding 3.5 percent. The steel will sell for $25 a ton. Assume the steel can be made from any combination of three different alloys, whose properties are given below.
Nickel Manganese Carbon Cost per Ton
Alloy 1 5% 8% 1% $18
Alloy 2 4 2 3 15
Alloy 3 2 2 5 10
Determine the most profitable blend of alloys that will satisfy the requirements. Hints: Let your control variables be as follows: x1 is the number of tons of alloy 1 used to make the steel, x2 is the number of tons of alloy 2 used to make the steel, and x3 is the number of tons of alloy 3 used to make the steel. The percent nickel in the steel can be calculated from the ratio of the tons of nickel in the steel divided by the total tons of steel or 100*(0.05x1 + 0.04x2 + 0.02x3)/(x1 + x2 + x3).