5.The Charm City Manufacturing Company manufactures a product in an assembly lineoperation. One of the machines on the line is a drill press that has a singleassembly line feeding into it. A partially completed unit arrives at the pressto be worked on every 8 minutes, on average. The machine operator can processan average of 10.5 units per hour. Assume it is a single-server waiting linemodel.

(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 average number ofunits in the queue and the average number of units in the system.

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

(e)Find the utilization factor of the operator.

6.In Question 5, suppose the current operator can be replaced by a more efficientnew operator, but the new operator is paid $28 per hour whereas the currentoperator is paid $22 per hour. The new operator can process 12.2 units perhour. If a units time is considered to be worth $12 per hour, is it worth toreplace the current operator with the new operator?