Problem 12-1
STAR Co. provides paper to smaller companies whose volumes arenot large enough to warrant dealing directly with the paper mill.STAR receives 100-feet-wide paper rolls from the mill and cuts therolls into smaller rolls of widths 12, 15, and 30 feet. The demandsfor these widths vary from week to week. The following cuttingpatterns have been established:
| Number of: |
| Pattern | 12ft. | 15ft. | 30ft. | Trim Loss |
| 1 | 2 | 3 | 4 | 5 ft. |
| 2 | 6 | 7 | 8 | 9 ft. |
| 3 | 10 | 11 | 12 | 13 ft. |
| 4 | 14 | 15 | 16 | 17 ft. |
| 5 | 18 | 19 | 20 | 21 ft. |
Trim loss is the leftover paper from a pattern (e.g., forpattern 4, 14(12) + 15(15) + 16(30) = 83 feet used resulting in100-83 = 17 foot of trim loss). Demands this week are 22 12-footrolls, 23 15-foot rolls, and 24 30-foot rolls. Develop anall-integer model that will determine how many 100-foot rolls tocut into each of the five patterns in order to meet demand andminimize trim loss (leftover paper from a pattern).
Optimal Solution:
| Pattern | Number Rolls Used |
| 1 | |
| 2 | |
| 3 | |
| 4 | |
| 5 | |
Trim Loss: feet
