STAR Co. provides paper to smaller companies whose volumes are not large enough to warrant dealing directly with the paper mill. STAR receives 100feetwide 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:
Number of:  
Pattern  12ft.  15ft.  30ft.  Trim Loss 
1  0  0  3  10 ft. 
2  0  6  0  10 ft. 
3  3  4  0  4 ft. 
4  3  0  2  4 ft. 
5  2  5  0  1 ft. 
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 10096 = 4 foot of trim loss). Demands this week are 5,686 12foot rolls, 1,660 15foot rolls, and 3,490 30foot rolls. Develop an allinteger model that will determine how many 100foot 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:
Pattern  Number Rolls Used 
1 =  
2 = 

3 =  
4 =  
5 = 
Trim Loss: __ feet
Xi: Number of rolls cut from pattern i
i belongs to [1,2,3,4,5]
Objective function (Minimize T)
T= 10*X1+ 10*X2+ 4*X3 +4*X4 + x5
12*(3* X3+3* X4+2* X5)>=5686*12
15*(6* X2+4* X3+ 5* X5)>=1660*15
30*(3* X1+2* X4)>=3490*30
Xi>=0, Xi is an integer
Pattern 
No of rolls used 
1 
0 
2 
0 
3 
0 
4 
1745 
5 
332 
Trim Lost= 7312 feet
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