A paper mill sells rolls of paper to newspapers, which usually place orders for rolls of different widths. The mill has just received a large order for 1.5 million feet of 4-foot-wide paper, 6 million feet of 9-foot-wide paper, and 3 million feet of 12-foot¬wide paper. It produces rolls of two sizes: (1) 3,000 feet long and 14 feet wide, at a cost of $600 per roll, and (2) 3,000 feet long and 20 feet wide, at a cost of $1,100 per roll. Large cutting machines are then used to cut these rolls to rolls of desired widths.
(a) What should the paper mill do to satisfy this order at minimum cost? Hint: You need to first identify the different ways in which 14-foot¬wide and 20-foot-wide rolls can be cut into 4-, 9-, and 12-foot-wide rolls.