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:

Trim loss is the leftover paper from a pattern (for example, for pattern 4, 2(12) + 1(15) 1 2(30) = 99 feet used results in 100 €“ 99 = 1 foot of trim loss). Demands this week are 5670 12-foot rolls, 1680 15-foot rolls, and 3350 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).

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Pattern Number 12-ft 0 0 15-ft 30-ft Trim Loss (ft) 10 10 4 0 0 0