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:

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 cutting patterns have been established: Trim loss is the leftover paper from a pattern (e.g., for pattern 4,3(12)+2(15)+1(30)=96 feet used resulting in 10096=4 foot of trim loss). Orders in hand for the coming week are 5,670 12-foot rolls, 1,680 15-foot rolls, and 3,350 30-foot rolls. Any of the three types of rolls in hand will be sold on the open market at the selling price. No inventory is held. (a) Formulate an integer programming model that will determine how many 100 -foot rolls to cut into each of the fine in your answer is zero enter " 0 " and if the constant is " 1 " it must be entered in the box. Let xj= number of 100 -foot-wide rolls using cutting pattern j,j=1,2,3,4,5. Optimal Solution: (b) Solve the model formulated in part a. What is the minimal amount of trim loss? Total Trim Loss: feet