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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
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter7: Nonlinear Optimization Models
Section: Chapter Questions
Problem 56P
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I need the number of rolls sold on the open market in 12 foot rolls. From the image 

8 ⒸHE ? 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 ✔ X 2 x 2 x 2 x 2 + + + + 7 4 1 1 X3 X3 + + ✓ + 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 X 3 X1, X2, X3, X 4, X 5 are integers and nonnegative X5 2 Z Z ✓ ✓ Q Search this course X 5670 1680 3350 12-foot rolls 15-foot rolls 30-foot rolls A-Z Ce * €
Transcribed Image Text:8 ⒸHE ? 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 ✔ X 2 x 2 x 2 x 2 + + + + 7 4 1 1 X3 X3 + + ✓ + 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 X 3 X1, X2, X3, X 4, X 5 are integers and nonnegative X5 2 Z Z ✓ ✓ Q Search this course X 5670 1680 3350 12-foot rolls 15-foot rolls 30-foot rolls A-Z Ce * €
• 8 Ⓒ ? U 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 w #
Transcribed Image Text:• 8 Ⓒ ? U 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 w #
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Practical Management Science
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ISBN:
9781337406659
Author:
WINSTON, Wayne L.
Publisher:
Cengage,
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