widths vary from week to week. The following cutting patterns have been established:

rolls produced in excess of the orders in hand will be sold on the open market at the selling price. No inventory is held. Let $\backslash ($ x$\_\{$j$\}=\backslash )$ number of $100-$foot$-$wide rolls using cutting pattern $\backslash ($ j$,$ j$=1,2,3,4,5\backslash ).$

Optimal Solution:

$($b$)$ Solve the model formulated in part a$.$ What is the minimal amount of trim loss?

Total Trim Loss: feet

How many of each pattern should be used and how many of each type of roll will be sold on the open market? If your answer is zero enter $"0".$

Number of Rolls Sold

Type of Roll on the Open Market

$12-$foot rolls

$15-$foot rolls

$30-$foot rolls