On average, 40 jobs arrive per day at a factory. The time between arrivals of jobs is exponentially distributed. The factory can process an average of 42 jobs per day, and the time to process a job is exponentially distributed.
a. On average, how long does it take before a job is completed (measured from the time the job arrives at the factory)?
b. What fraction of the time is the factory idle?
c. What is the probability that work on a job will begin within two days of its arrival at the factory?