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:

The aluminum content must be at least 3% and at most 6%

The silicon content must lie between 3% and 5%

The carbon content must be between 3% and 7%

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.