The Gem City Paper Company produces rolls of paper of various types for its customers. One type is produced in standard rolls that are 50 inches wide and 100 yards long. Customers of this type of paper order rolls that are 100 yards long but can have any of the widths 12, 15, 25, 30, and 40 inches. In a given week, Gem City Paper waits for all orders and then decides how to cut its 50-inch rolls to satisfy the orders. The weekly number of orders for each roll width is provided in the table below. Each week this company must decide how to cut its rolls in the most economical way to meet its orders. Specifically, it wants to produce and cut as few rolls as possible. Formulate and solve an IP model to help Gem City Paper find the best way to meet all weekly customer demands. (Hint: list all the feasible patterns that can be used to cut a 50-inch roll of paper). Width 12 15 25 30 40 Requirement 40 30 20 20 20
The Gem City Paper Company produces rolls of paper of various types for its customers. One type is produced in standard rolls that are 50 inches wide and 100 yards long. Customers of this type of paper order rolls that are 100 yards long but can have any of the widths 12, 15, 25, 30, and 40 inches. In a given week, Gem City Paper waits for all orders and then decides how to cut its 50-inch rolls to satisfy the orders. The weekly number of orders for each roll width is provided in the table below. Each week this company must decide how to cut its rolls in the most economical way to meet its orders. Specifically, it wants to produce and cut as few rolls as possible. Formulate and solve an IP model to help Gem City Paper find the best way to meet all weekly customer demands.
(Hint: list all the feasible patterns that can be used to cut a 50-inch roll of paper).
| Width | 12 | 15 | 25 | 30 | 40 |
| Requirement | 40 | 30 | 20 | 20 | 20 |
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