A classic linear programming problem involves minimizing trim loss. Here is one version of the problem: A mill cuts 20-foot pieces of wood into several different lengths: 8-foot, 10-foot and 12-foot. The mill has a certain amount of 20-foot stock on hand and orders for the various sizes. The objective is to fill the orders with as little waste as possible. For example, if two 8-foot lengths are cut from a 20-foot piece, there will be a loss of 4 feet, the leftover amount. Currently, the mill has 350 20-foot pieces of wood on hand and the following orders, which must be filled from stock on hand: Size in feet 8 10 12 Number Ordered 276 100 250 a. Formulate algebraically an LP model that will enable the mill operator to satisfy the orders with minimum trim loss. (Hint: List the different ways the 20-foot pieces could be cut into the desired sizes.) (10 points) b. Using your notation from a, write an equation for i. The amount of waste that would result given a solution. (1 point) ii. The number of pieces of each size (8-foot, 10-foot, and 12-foot). (2 points) c. Formulate this same linear programming problem on a spreadsheet and SOLVE using Excel Solver (Provide the corresponding Excel Spreadsheet and the Answer Report). Include managerial statements that communicate the results of the analyses, (i.e. describe verbally the results). (7 points)