STAR Co. provides paper to smaller companies whose volumes are not large enough to warranpaper rolls from the mill and cuts the rolls into smaller rolls of widths 12, 15, and 30 feet. Thecutting patterns have been established:12Pattern 12ft. 15ft. 30ft. Trim Loss04110 ft.307 ft.8004 ft.2121 ft.52311 ft.Trim loss is the leftover paper from a pattern (e.g., for pattern 4, 2(12)+1(15) + 2(30) = 99hand for the coming week are 5,670 12-foot rolls, 1,680 15-foot rolls, and 3,350 30-foot rolls.hand will be sold on the open market at the selling price. No inventory is held.Number of:3 (a) Formulate an integer programming model that will determine how many 100-foot rolls toyour answer is zero enter "0" and if the constant is "1" it must be entered in the box.Let x-number of 100-foot-wide rolls using cutting pattern/./- 1, 2, 3, 4, 5.Optimal SolutionMin4.L.Pattern101X12S+2891671©* ©322*2Ⓡ3→0©Number of Rolls SoldType of Roll on the Open Market12-foot rolls*3*3>*3+(b) Solve the model formulated In part a. What is the minimal amount of trim loss?Total Trim Loss2835 feet1How many of each pattern should be used and how many of cach type of roll will be sold aNumber of Rolls Usedfor Each Pattern2X434X4X4XXX, X, Xs are integers and nonnegat

Decision Variables: Suppose-xj= No. of 100 foot wide rolls using cutting pattern j, where…

Answered: STAR Co. provides paper to smaller…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter14: Data Mining

Section14.2: Classification Methods

Problem 11P

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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. Pattern Number 12‐ft 15‐ft 30‐ft Trim Loss (ft) 1 0 6 0 10 2 0 0 3 10 3 8 0 0 4 4 3 0 2 4 5 7 1 0 1 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, 1,670 15-foot rolls, and 3,340 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. (a) Formulate an integer programming model that will determine how many 100-foot rolls to cut into each of the…
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