Consider a single-server system with two types of jobs. The system has a limited capacity of three total jobs in the system at any time. The job classes have different mean arrival and service rates, but all are assumed to be exponentially distributed. Let 1 be the mean arrival rate and 1 be the mean service rate of Job Type 1, and let 2 be the mean arrival rate and 2 be the mean service rate of Job Type 2. Jobs are served on a non-preemptive priority basis with job type 1 given preference; that is, once a job starts it cannot be displaced from the machine. (a) Develop the labeled directed arc network for this system. Hint: there are thirteen different states and the sequence of job types in the queue will always be Type 1s in front of Type 2s. (b) Write the equations linking the steady-state probabilities. (c) Write a formula for computing (in terms of the pis) the total WIPs, WIPs by product type, throughput, throughput by product type, the system CTs, and CTs by product type.