Consider a two-stage system. The first stage performs a punching operation with a batch size of k jobs. The setup starts after a batch is ready. Then, the jobs are punched one by one. The setup time is . The mean of the process time is 1 per job and the CV is 1. Jobs arrive in batches of k units every time units and the corresponding CV is . After the punching operation is completed, the whole batch is transferred to the second stage. The second stage consists of a single painting machine. This machine does painting for each job. The painting time per job on average is 2 and the CV is 2. Additionally, this machine suffers from a pre-emptive outage with MTTF () and MTTR (). The CV of the repair time is (). After a job is painted, the job leaves Stage 2. Please first give the conditions under which the system is stable. Then, under these conditions, please write down the formula for the average number of jobs in the system. Note that if you want to use some other symbols in your formulas, you have to clearly define them based on the notation given in this question.