A paper mill produces rolls of paper used in making cash registers.Each roll of paper is
100m in length and can be used in widths of
3,4,6 and
10cm.The company's production process results in rolls that are
24cm in width.Thus, the company must cut its
24cm roll to the desired widths.It has six basic cutting alternatives as follows:
Cutting alternatives | Width of Rolls(cm) 3 | Width of Rolls(cm) 4 | Width of Rolls(cm) 6 | Width of Rolls(cm) 10 | Waste(cm) |
1 | 4 | 3 | - | - | - |
2 | - | 3 | 2 | - | - |
3 | 1 | 1 | 1 | 1 | 1 |
4 | - | - | 2 | 1 | 2 |
5 | - | 4 | 1 | - | 2 |
6 | 3 | 2 | 1 | - | 1 |
The minimum demand for the four rolls is as follows:
Roll width(cm) | Demand |
2 | 2,000 |
4 | 3,600 |
6 | 1,600 |
10 | 500 |
The paper mill wishes to minimize the waste resulting from trimming to size.Formulate the L.P model.