The Rheem Paper Company produces rolls of paper of various types for its customers. One type is produced in standard rolls that are 60 inches wide and (when unwound) 200 yards long. Customers for this...

The Rheem Paper Company produces rolls of paper of various types for its customers. One type is produced in standard rolls that are 60 inches wide and (when unwound) 200 yards long. Customers for this type of paper order rolls that are all 200 yards long, but can have any of the widths 12, 15, 20, 24, 30, or 40 inches. In a given week, Rheem waits for all orders and then decides how to cut its 60-inch rolls to satisfy the orders. For example, if there are 5 orders for 15-inch widths and 2 orders for 40-inch widths, Rheem could satisfy the order by producing 3 rolls, cutting each of the first two into a 40-inch and a 15- inch cut (with 5 inches left over) and cutting the third into 4 15-inch cuts (with one of these left over). Each week, Rheem must decide how to cut its rolls in the most economical way to meet its orders. Specifically, it wants to produce as few rolls as possible.

Objective To find a way of cutting paper rolls in various widths so as to satisfy all customer orders and minimize the total number of rolls cut.