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

the following:

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?