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TAR Co. provides paper to smaller companies with volumes that 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. Min s.t. 12-ft Pattern Number 15-ft 30-ft 1 2 P₁ P2 P3 P4 P5 20 3 4 5 12-ft 15-ft 30-ft 0 0 8 3 7 6 0 0 0 1 0 3 0 2 0 Trim Loss (ft) Trim loss is the leftover paper from a pattern (e.g., for pattern 4, 3(12) + 0(15) + 2(30) = 96 feet used results in 100- 96= 4 foot of trim loss). Orders in hand for the coming week are 5,680 12- foot rolls, 1,690 15-foot rolls, and 3,360 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. 10 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. (Let P, = number of rolls cut into pattern/, for = 1, 2, 3, 4, 5.) 10 4 4 1

TAR Co. provides paper to smaller companies with volumes that 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. Min s.t. 12-ft Pattern Number 15-ft 30-ft 1 2 P₁ P2 P3 P4 P5 20 3 4 5 12-ft 15-ft 30-ft 0 0 8 3 7 6 0 0 0 1 0 3 0 2 0 Trim Loss (ft) Trim loss is the leftover paper from a pattern (e.g., for pattern 4, 3(12) + 0(15) + 2(30) = 96 feet used results in 100- 96= 4 foot of trim loss). Orders in hand for the coming week are 5,680 12- foot rolls, 1,690 15-foot rolls, and 3,360 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. 10 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. (Let P, = number of rolls cut into pattern/, for = 1, 2, 3, 4, 5.) 10 4 4 1

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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STAR Co. provides paper to smaller companies with volumes that 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. Min s.t. 12-ft Pattern Number 15-ft 30-ft 1 2 P1, P2, P3 P4 P5 ≥ 0 3 4 5 12-ft 15-ft 30-ft Trim Loss (ft) 0 0 8 3 7 6 0 0 0 1 C 3 0 2 0 10 Trim loss is the leftover paper from a pattern (e.g., for pattern 4, 3(12) + 0(15) + 2(30) = 96 feet used results in 100 - 96 = 4 foot of trim loss). Orders in hand for the coming week are 5,680 12- foot rolls, 1,690 15-foot rolls, and 3,360 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. 10 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. (Let P, = number of rolls cut into pattern /, for i = 1, 2, 3, 4, 5.) 4 4 ASK YOUR TEACHER 1
Transcribed Image Text:STAR Co. provides paper to smaller companies with volumes that 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. Min s.t. 12-ft Pattern Number 15-ft 30-ft 1 2 P1, P2, P3 P4 P5 ≥ 0 3 4 5 12-ft 15-ft 30-ft Trim Loss (ft) 0 0 8 3 7 6 0 0 0 1 C 3 0 2 0 10 Trim loss is the leftover paper from a pattern (e.g., for pattern 4, 3(12) + 0(15) + 2(30) = 96 feet used results in 100 - 96 = 4 foot of trim loss). Orders in hand for the coming week are 5,680 12- foot rolls, 1,690 15-foot rolls, and 3,360 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. 10 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. (Let P, = number of rolls cut into pattern /, for i = 1, 2, 3, 4, 5.) 4 4 ASK YOUR TEACHER 1
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