Sharp Discounts Wholesale Club encompasses two service desks with one server at each desk. There is one desk at each entrance of the store. Customers arrive at each service desk at an average of one every 6 minutes following the Poisson distribution. The average service time at every service desk is 216 seconds per customer following the exponential service distribution.
a) Determine the total number of customers, on average, is waiting in line in front of each service desk?
b) Determine the total time does a customer expend at the service desk either waiting for the help or receiving help?
c) Looking at just one of the service desks, find out the probability that there are at least three customers waiting in the line when the next individual arrives at service desk?
d) Sharp is now considering consolidating its two service desks to one location, staffed by two clerks. The clerks will persist to work at the same individual speed of 216 seconds per customer. Determine the number of customers, on average, is waiting in line? How much total time does a customer expend at the service desk?
e) Do you think the Sharp Discounts Wholesale Club must consolidate the service desks? Your discussion should consider both the economics and the customer service features of this waiting line operation. There would be no additional cost for moving the two operations to one operation. The clerks would persist to be paid similar as they were paid at the single desk operation.
f) Assume that it is no longer needed that the clerks be paid the similar under either operation. The clerks beneath the consolidated operation are each paid $30 per hour and the estimated cost to Sharp for time a customer is at service desk either waiting or being helped is $1 per minute. Find out the maximum hourly rate that each of the clerks can be paid beneath the two service desk operation and hence the total cost of the operation is similar for either arrangement. Suppose that there is no cost for consolidating the service.