(Looking for number of rolls used. Please show how you get the answer.) STAR Co.
ID: 3216440 • Letter: #
Question
(Looking for number of rolls used. Please show how you get the answer.)
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, 3(12) + 0(15) + 2(30) = 96 feet used resulting in 100-96 = 4 foot of trim loss). Demands this week are 5,692 12-foot rolls, 1,719 15-foot rolls, and 3,250 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 10 ft. 2 0 2 2 10 ft. 3 4 1 1 7 ft. 4 3 0 2 4 ft. 5 2 5 0 1 ft.Explanation / Answer
let x1,x2,x3,x4,x5 be the number of 100 feet rolls to be cut into pattern 1,2,3,4,5
min:10x1+10x2+7x3+4x4+x5
s.t:
4x3+3x4+2x5>=5692
6x1+2x2+x3+6x5>=1719
2x2+x3+2x4>=3250
optimal solution
x1=0,x2=0,x3=0,x4=1625,x5=817/2=408
Optimal Solution:
Pattern Number Rolls Used 1 ___________0_____ 2 ___________0_____ 3 ___________0_____ 4 __________1625______ 5 ___________408_____Related Questions
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