13. Jobs enter a job shop in random fashion according to a Poisson process at a stationary overall rate, two every 8-hour day. The jobs are of four types. They flow from work station to work station in a fixed order, depending on type, as shown below. The proportions of each type are also shown. Type 1 234 Type 1 2 Processing times per job at each station depend on type, but all times are, approximately, normally distributed with mean and s.d. in hours as follows: 3 Flow through Stations 1, 2, 3, 4 1, 3, 4 2,4,3 1,4 4 1 (20,3) (18,2) (30.5) Station Proportion 0.4 0.3 0.2 0.1 2 (30,5) (20, 2) 3 (75.4) (60, 5) (50, 8) 4 (20,3) (10, 1) (10, 1) (15, 2) Station i will have c; workers, i = 1, 2, 3, 4. Each job occupies one worker at a station for the duration of a processing time. All jobs are processed on a first-in-first-out basis, and all queues for waiting jobs are assumed to have unlimited capacity. Simulate the system for 800 hours, preceded by a 200-hour initialization period. Assume that c 8. C2 = 8, C3 = 20, C4 = 7. Based on R = 20 replications, compute a 95% confidence interval for average worker utilization at each of the four stations. Also, compute a 95% confidence interval for mean total response time for each job type, where a total response time is the total time that a job spends in the shop. S 13. Jobs enter a job shop in random fashion according to a Poisson process at a stationary overall rate, two every 8-hour day. The jobs are of four types. They flow from work station to work station in a fixed order, depending on type, as shown below. The proportions of each type are also shown. Type 1 234 Type 1 2 Processing times per job at each station depend on type, but all times are, approximately, normally distributed with mean and s.d. in hours as follows: 3 Flow through Stations 1, 2, 3, 4 1, 3, 4 2,4,3 1,4 4 1 (20,3) (18,2) (30.5) Station Proportion 0.4 0.3 0.2 0.1 2 (30,5) (20, 2) 3 (75.4) (60, 5) (50, 8) 4 (20,3) (10, 1) (10, 1) (15, 2) Station i will have c; workers, i = 1, 2, 3, 4. Each job occupies one worker at a station for the duration of a processing time. All jobs are processed on a first-in-first-out basis, and all queues for waiting jobs are assumed to have unlimited capacity. Simulate the system for 800 hours, preceded by a 200-hour initialization period. Assume that c 8. C2 = 8, C3 = 20, C4 = 7. Based on R = 20 replications, compute a 95% confidence interval for average worker utilization at each of the four stations. Also, compute a 95% confidence interval for mean total response time for each job type, where a total response time is the total time that a job spends in the shop. S