8. (20 points) Consider the four-stage process shown below. Defects from stage 2 have to be reprocessed at stage 2. Defects from stage 4 are scrapped with probability 1-Q and reworked at stage 3 with probability Q. The probability of a part being defective at stage 2 is P1 and the probability of a part being defective at stage 4 is P2. Let I denote the input into stage 1 and let O denote the output of good product from stage 4. 4 2 3 1 P2 Pi Q 1-Q a. If we want steady state production of k units per hour, which machine has to process the most parts? Scrap b. Represent the steady state output of the process (good product leaving stage 4) as a function of I, P1, P2, and Q. c. What is the steady state scrap rate of the process as a function of I, P1, P2, and Q?