# math / linear programming

posted by
**Tim**
.

Two factories manufacture 3 different grades of paper. The company that owns the factories has contracts to supply at least 16 tons of low grade, 5 tons of medium grade, and at least 20 tons of high grade paper. It costs $1000 per day to operate the first factory and $2000 per day to operate the second. Factory 1 produces 8 tons of low grade, 1 ton of medium grade, and 2 tons of high grade paper in one day's operation. Factory 2 produces 2 tons of low grade, 1 ton of medium grade, and 7 tons of high grade paper per day. How many days should each factory be in operation in order to fill the orders most economically?