Problen 12-1 STAR Co. provides paper to smaller companies whose volumes are not

Question

Problen 12-1 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 outs 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 10 ft. 10 ft 4 ft 4 1t. 1 ft. 5 2 0 3 0 2 2 5 0 Trim loss is the leftover paper from a pattern (e.g., for pattem 4, 3(12)2(15)1(30)-96 feet used resulting in 100-96 4 foot of trim loss). Demands this week are 5,92 12-foct rolls, 1,650 15-foot rolls, and 3,430 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 Sclutionn: Pattern Number Rolls Used Trim LosS feet

Explanation / Answer

Let a,b,c,d,e be the quantities of pattern 1,2,3,4,5

Minimize Z = 10a+10b+10c+4d+1e such that

5a+3c+3d+2e=5692

2a+2b+2d+5e=1650

2b+2c+1d=3430

This equation can be solved to get the answer.

The optimal solution value is Z = 7356.5263157895
X1 = 0
X2 = 29.736842105263
X3 = 1685.2631578947
X4 = 0
X5 = 318.10526315789

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