An industrial recycling center uses two scrap aluminum metals, A and B, to produce a special alloy. Scrap A contains 6% aluminum, 3% silicon and 4% carbon. Scrap B has 3% aluminum, 6% silicon and 3% carbon.
The costs per ton for scraps A and B are $100 and $80, respectively. The specifications of the special alloy require that (1) the aluminum content must be at least 3% and at most 6%, (2) the silicon content must lie between 3% and 5%, and (3) the carbon content must lie between 3% and 7%.
Determine the optimum mix of the scraps that should be used in producing 1000 tons of the alloys.