Two operators handle adjustments for a group of 10 machines. Adjustment time is exponentially distributed and has a mean of 14 minutes per machine. The machines operate for an average of 86 minutes between adjustments. While running, each machine can turn out 50 pieces per hour. Find:
a. The probability that a machine will have to wait for an adjustment.
b. The average number of machines waiting for adjustment.
c. The average number of machines being serviced.
d. The expected hourly output of each machine, taking adjustments into account.
e. Machine downtime represents a cost of $70 per hour; operator cost (including salary and fringe benefits) is $15 per hour. What is the optimum number of operators?