STAR Co. provides paper to smaller companies whose volumes are not large enough
ID: 2923389 • Letter: S
Question
STAR Co. provides paper to smaller companies whose volumes are not large enough to warrant dealing directly with the paper mill. STAR receives 100-feet-wide paper rolls from the mill and cuts the rolls into smaller rolls of widths 12, 15, and 30 feet. The demands for these widths vary from week to week. The following cutting patterns have been established:
Trim loss is the leftover paper from a pattern (e.g., for pattern 4, 2(12) + 1(15) + 2(30) = 99 feet used resulting in 100-99 = 1 foot of trim loss). Demands this week are 5,684 12-foot rolls, 1,720 15-foot rolls, and 3,240 30-foot rolls. Develop an all-integer model that will determine how many 100-foot rolls to cut into each of the five patterns in order to meet demand and minimize trim loss (leftover paper from a pattern).
Optimal Solution:
Number of: Pattern 12ft. 15ft. 30ft. Trim Loss 1 0 6 0 11 ft. 2 0 0 2 11 ft. 3 7 0 0 4 ft. 4 2 1 2 1 ft. 5 7 1 0 1 ft.Explanation / Answer
Option 2 has trim loss of 4134 ft with 1 12 ft roll produced in excess meeting exactly the requirement for 15 & 30 ft rolls
While option 1 has a trim loss of 2213 ft however producing in excess 1 12 ft roll & 1071 15 ft rolls
Option 2 seems optimal unless the excess production is kept in stock anticipating another order to be fulfilled
100 ft. No.'s
12 ft.
15 ft.
30 ft.
Trim Loss
Requirement
5680
1720
3270
Pattern 1
0
0
0
0
0
Pattern 2
0
0
0
0
0
Pattern 3
0
0
0
0
0
Pattern 4
1635
1635
1635
3270
1635
Pattern 5
578
4046
1156
0
578
TOTAL
5681
2791
3270
2213
Excess
-1
-1071
100 ft. No.'s
12 ft.
15 ft.
30 ft.
Trim Loss
Requirement
5680
1720
3270
Pattern 1
17
0
85
0
187
Pattern 2
0
0
0
0
0
Pattern 3
578
4046
0
0
2312
Pattern 4
1635
1635
1635
3270
1635
Pattern 5
0
0
0
0
0
TOTAL
5681
1720
3270
4134
Excess
-1
0
0
Hope this will be helpful. Thanks and God Bless you:-) Thumbs up if this will helpful.
100 ft. No.'s
12 ft.
15 ft.
30 ft.
Trim Loss
Requirement
5680
1720
3270
Pattern 1
0
0
0
0
0
Pattern 2
0
0
0
0
0
Pattern 3
0
0
0
0
0
Pattern 4
1635
1635
1635
3270
1635
Pattern 5
578
4046
1156
0
578
TOTAL
5681
2791
3270
2213
Excess
-1
-1071
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.