2. EMORY ALUMINUM The Emory Aluminum company rolls and sells aluminum foil in several widths. (Length is the same for all orders). Customers can order rolls of foil 24 inches, 20 inches, 12 inches, or 8 inches wide. The foil is manufactured in a standard width of 54 inches, and the smaller widths are slit(cut) from the standard roll. There are many ways the smaller widths can be cut, as shown in the table below: CUTTING METHOD 1 2 4 5 6 7 8 9 10 11 12 13 24 inches 2 1 1 1 1 20 inches 1 2 1 1 1 12 inches 1 1 1 4 8 inches 1 2 3 1 1 2 4 3 SCRAP 6. 2 2 6 6 2 6. 2 6. 2 6 6. (inches) For example, using method 3, one roll 24 inches wide, one roll 12 inches wide and two rolls 8 inches wide are cut from the standard roll. This leaves 2 inches of scrap [54 24- 12- 2(8) = 2]. Because some scrap is generated by the slitting process, it is not possible to cut certain combinations (not shown). All rolls for cutting are a standard 54-inch width, and all orders are for the standard widths in the table. Emory has received the following orders for the month of July: WIDTH ROLLS ORDERED 24 INCHES 330 20 INCHES 120 12 INCHES 480 8 INCHES 160 How should Emory cut rolls to fill these orders and minimize scrap? Formulate a linear programming model for the problem in a word document and then use solver to find a solution. 66 2. 2. 3.