A company has three types of processing machines, each of which has different speed and defect rates. Type I machines can produce 20 parts per hour with 5% defective parts; type II, 15 pieces per hour with 10% defects and type III, 10 pieces per hour without defects. The hourly cost of machine operation is $ 2.00; US $ 1.75 and US $ 1.50, respectively. Must 3500 parts can be processed per day (8 hours / day), but only 8 machines are available type I, 10 type II and 20 type III. Each defective part costs the company US $ 1.00. Formulate a PL model to determine the optimal solution for this problem.