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: Number of: Pattern $12$ft$.15$ft$.30$ft$.$ Trim Loss $10$ ft$.10$ ft$.7$ ft$.4$ ft$.1$ 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 $100-964$ foot of trim loss$).$ Demands this week are $5,69212-$foot rolls, $1,71915-$foot rolls, and $3,25030-$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: Pattern Number Rolls Used Trim Loss: feet