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 are as follows:
A. The aluminum content must be at least 3% and at most 6%.
B. The silicon content must lie between 3% and 5%.
C. The carbon content must be between 3% and 7%.
D. Formulate a linear program that can be used to determine the amounts of scrap A and B that should be used to minimize the cost of creating 1000 tons of the special alloy.