esults in 100 – 99 = 1 foot of trim loss). Orders in hand for the coming week are 5,670 12-foot olls, 1,680 15-foot rolls, and 3,350 30-foot rolls. Any of the three types of rolls produced in excess f the orders in hand will be sold on the open market at the selling price. No inventory is held. a. Formulate an integer programming model that will determine how many 100-foot rolls to cut into each of the five patterns in order to minimize trim loss. b. Solve the model formulated in part (a). What is the minimal amount of trim loss? How many of each pattern should be used and how many of each type of roll will be sold on the open market?

At the beginning of each week, a machine is in one of four conditions: 1 = excellent; 2 = good; 3 = average; 4 = bad. The weekly revenue earned by a machine in state 1, 2, 3, or 4 is 100, 90, 50, or 10, respectively. After observing the condition of the machine at the beginning of the week, the company has the option, for a cost of 200, of instantaneously replacing the machine with an excellent machine. The quality of the machine deteriorates over time, as shown in the file P10 41.xlsx. Four maintenance policies are under consideration: Policy 1: Never replace a machine. Policy 2: Immediately replace a bad machine. Policy 3: Immediately replace a bad or average machine. Policy 4: Immediately replace a bad, average, or good machine. Simulate each of these policies for 50 weeks (using at least 250 iterations each) to determine the policy that maximizes expected weekly profit. Assume that the machine at the beginning of week 1 is excellent.