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)

THE OBJECTIVE IS TO MINIMIZE THE WASTE WHILE MEETING DEMAND (has to be feasible)