Problem 3 (14 points)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 left over 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	Number Order
8	276
10	100
12	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.) (8 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).(1 point)

c. Formulate this same linear programming problem on a spreadsheet and SOLVE using Excel solver (Provide a printout of the correspondingExcel Spreadsheet and the Answer Report). Include managerial statements that communicate the results of the analyses (i.e. describe verbally the results). (4 points)