Suppose the current operator can be replaced by a more efficient new operator, but the new operator is paid $30 per hour whereas the current operator is paid $24 per hour. The new operator can process 10.2 units per hour. If a unit’s time is considered to be worth $10 per hour, is it worth to replace the current operator with the new operator? Calculate the total cost of the current operator and the units’ time and the total cost of the more efficient new operator and the units’ time to answer this question.

The Charm City Manufacturing Company manufactures a product in an assembly line operation. One of the machines on the line is a drill press that has a single assembly line feeding into it. A partially completed unit arrives at the press to be worked on every 7.5 minutes, on average. The machine operator can process an average of 9.4 units per hour. Assume it is a single-server waiting line model.

(a) Determine the mean arrival rate and the mean service rate.

(b) Determine the probability that a unit will have an empty queue.

(c) Determine the probability that 3 units are in the queuing system.

(d) Determine the average number of units in the queue and the average number of units in the system.

(e) Determine the average waiting time in the queue and the average total time in the system for a unit.

(f) Find the utilization factor of the machine operator.