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3. (20 pts) Let's suppose an Arena model has been developed to simulate a machine shop composed of ten machines (MACHINE 1, ... MACHINE 10). The machine shop opens from 8 am to 5 pm. (The machines continues to operate after 5 for another hour to finish up the work arriving before 5). The goal of the simulation study is to estimate the utilization of each machine. Answer the following three questions. (a) (10 pts) The table shown below represents the machine status (0: idle, 1: busy) of MACHINE 1 over time obtained from simulation runs. Note that five replications have been used as a starting point. Given these simulation output data in the table, compute a 95% confidence interval for the machine utilization of MACHINE 1. (note: 10.975 is 2.78 when n = 4, and to 975 is 2.06 when n = 24.) 5-6 time 8-9 9-10 10-11 11-12 12-1 1-2 2-3 3-4 4-5 replications 11100 111 2 1 1 1 1 1 1 1 0 0 0 1 1 31 1 1 1 1 0 0 0 0 4 1 1 0 0 0 0 0 1 5 1 0 0 0 0 0 0 1 (b) (10 pts) In problem (a), you have computed a confidence interval for the machine utilization. Suppose we intend to keep the half width smaller than 0.05. Based on your result from (a), compute the number of replications needed using the equation below: nen, 3. (20 pts) Let's suppose an Arena model has been developed to simulate a machine shop composed of ten machines (MACHINE 1, ... MACHINE 10). The machine shop opens from 8 am to 5 pm. (The machines continues to operate after 5 for another hour to finish up the work arriving before 5). The goal of the simulation study is to estimate the utilization of each machine. Answer the following three questions. (a) (10 pts) The table shown below represents the machine status (0: idle, 1: busy) of MACHINE 1 over time obtained from simulation runs. Note that five replications have been used as a starting point. Given these simulation output data in the table, compute a 95% confidence interval for the machine utilization of MACHINE 1. (note: 10.975 is 2.78 when n = 4, and to 975 is 2.06 when n = 24.) 5-6 time 8-9 9-10 10-11 11-12 12-1 1-2 2-3 3-4 4-5 replications 11100 111 2 1 1 1 1 1 1 1 0 0 0 1 1 31 1 1 1 1 0 0 0 0 4 1 1 0 0 0 0 0 1 5 1 0 0 0 0 0 0 1 (b) (10 pts) In problem (a), you have computed a confidence interval for the machine utilization. Suppose we intend to keep the half width smaller than 0.05. Based on your result from (a), compute the number of replications needed using the equation below: nen

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