Chapter 13 Assignment 2. 3. 4. 5. ● ● STAR Co. provides paper 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: Pattern 12ft. 15ft. 30ft. Trim Loss 1 5 0 1 10 ft. 3 1 2 3 4 5 0 4 1 302 250 Trim loss is the leftover paper from a pattern (e.g., for pattern 4, 3(12) + 0(15) + 2(30) = 96 feet used resulting in 100-96= 4 foot of trim loss). Orders in hand for the coming week are 5,670 12-foot rolls, 1,680 15-foot rolls, and 3,350 30-foot rolls. Any of the three types of rolls produced in excess of the orders in hand will be sold on the open market at the selling price. No inventory is held. Min s.t. Number of: 0 (a) Formulate an integer programming model that will determine how many 100-foot rolls to cut into each of the five patterns in order to minimize trim loss. If your answer is zero enter "0" and if the constant is "1" it must be entered in the box. Let x j = number of 100-foot-wide rolls using cutting pattern j, j = 1, 2, 3, 4, 5. Optimal Solution: 10 5 0 ✔ X1 ✔ + X1 10 ft. 7 ft. 4 ft. X1 X1 1 ft. + 10 0 0 3 ✔ x2 Sx₂ + X x2 X2 7 1 1 S X3 + + 4 ✔ XA 3x4 ox₁ + 0 (b) Solve the model formulated in part a. What is the minimal amount of trim loss? Total Trim Loss: 7036 feet S 1 x5 Z 2 5x5 Z 2 X5 X3 2x4 X1, X2, X3, X4, X 5 are integers and nonnegative 0 X5 2 ✔ ✔ 5670 1680 3350 12-foot rolls 15-foot rolls 30-foot rolls
Chapter 13 Assignment 2. 3. 4. 5. ● ● STAR Co. provides paper 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: Pattern 12ft. 15ft. 30ft. Trim Loss 1 5 0 1 10 ft. 3 1 2 3 4 5 0 4 1 302 250 Trim loss is the leftover paper from a pattern (e.g., for pattern 4, 3(12) + 0(15) + 2(30) = 96 feet used resulting in 100-96= 4 foot of trim loss). Orders in hand for the coming week are 5,670 12-foot rolls, 1,680 15-foot rolls, and 3,350 30-foot rolls. Any of the three types of rolls produced in excess of the orders in hand will be sold on the open market at the selling price. No inventory is held. Min s.t. Number of: 0 (a) Formulate an integer programming model that will determine how many 100-foot rolls to cut into each of the five patterns in order to minimize trim loss. If your answer is zero enter "0" and if the constant is "1" it must be entered in the box. Let x j = number of 100-foot-wide rolls using cutting pattern j, j = 1, 2, 3, 4, 5. Optimal Solution: 10 5 0 ✔ X1 ✔ + X1 10 ft. 7 ft. 4 ft. X1 X1 1 ft. + 10 0 0 3 ✔ x2 Sx₂ + X x2 X2 7 1 1 S X3 + + 4 ✔ XA 3x4 ox₁ + 0 (b) Solve the model formulated in part a. What is the minimal amount of trim loss? Total Trim Loss: 7036 feet S 1 x5 Z 2 5x5 Z 2 X5 X3 2x4 X1, X2, X3, X4, X 5 are integers and nonnegative 0 X5 2 ✔ ✔ 5670 1680 3350 12-foot rolls 15-foot rolls 30-foot rolls
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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I need the number of rolls sold on the open market in 12 foot rolls. From the image
Transcribed Image Text:8
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CENGAGE MINDTAP
Chapter 13 Assignment
2.
3.
4.
5.
●
●
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:
Pattern 12ft. 15ft. 30ft. Trim Loss
1
2
3
4
5
0
0 0
4
3
2
5 0
Trim loss is the leftover paper from a pattern (e.g., for pattern 4, 3(12) + 0(15) + 2(30) = 96 feet used resulting in 100- 96 = 4 foot of trim loss). Orders in hand for the coming week
are 5,670 12-foot rolls, 1,680 15-foot rolls, and 3,350 30-foot rolls. Any of the three types of rolls produced in excess of the orders in hand will be sold on the open market at the selling
price. No inventory is held.
5
Min
s.t.
Number of:
1
10
02
5
1
0
3
1
1
✔
(a) Formulate an integer programming model that will determine how many 100-foot rolls to cut into each of the five patterns in order to minimize trim loss. If your answer is zero
enter "0" and if the constant is "1" it must be entered in the box.
Let x j = number of 100-foot-wide rolls using cutting pattern j, j = 1, 2, 3, 4, 5.
Optimal Solution:
+
X 1
X 1
X1
X 1
10 ft.
+
+
10 ft.
+
7 ft.
4 ft.
1 ft.
10
0
0
3
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X 2
x 2
x 2
x 2
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+
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+
7
4
1
1
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X3
+
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X 3
+
✔
4
3
0
2
X 4
(b) Solve the model formulated in part a. What is the minimal amount of trim loss?
Total Trim Loss: 7036
feet
+
✔ +
X 4
X 4
+
✔ +
X 4
1
2
5
0
X5
X5
X5
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X1, X2, X3, X 4, X 5 are integers and nonnegative
X5
2
Z
Z
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Q Search this course
X
5670
1680
3350
12-foot rolls
15-foot rolls
30-foot rolls
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Transcribed Image Text:•
8
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CENGAGE MINDTAP
Chapter 13 Assignment
(b) Solve the model formulated in part a. What is the minimal amount of trim loss?
Total Trim Loss:
7036
How many of each pattern should be used and how many of each type of roll will be sold on the open market? If your answer is zero enter "0".
Number of Rolls Used
for Each Pattern
Pattern
1
2
3
4
5
15-foot rolls
Icon Key
30-foot rolls
✔ Hide Feedback
Partially Correct
0
0
0
Number of Rolls Sold
Type of Roll on the Open Market
12-foot rolls
1675
336
feet
0
✓
Q Search this course
X
Check My Work
A-Z
Office
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#
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