Solve the below:
Q: Luxor paper Mill produces so-called liner board in jumbo reels having a standard width of 70 inches. Each reel has a fixed length. Customers, however, order reels having smaller widths and the same fixed length as the larger reel. Today's orders are for 100 reels of 22-inch width, 125 reels of 20-inch width and 80 reels of 12-inch width. the smaller widths are to be cut from the larger standard size reel. For example, . Luxor can decide to slit a jumbo into two reels each 22 inches wide and one reel 20 inches wide. This leaves 6 inches of trim waste from the 70-inch jumbo. Luxor wants to manufacture today's orders as to minimize trim waste
i. Find every possible way to slit a 70-inch jumbo reel into combinations of 22-inch, 20-inch and 12-inch width reels (as illustrated by the above example combination). Compute the trim waste for each combination - (need only combinations with trim waste <12). Then define a variable X_i representing the number to be made from each combination,
ii. Formulate an LP model in order to determine the number of each combination to satisfy customer demand for each of the three reel sizes while minimizing total trim waste.