Calls arrive at a rate of 150 per hour to the 800 number for the Land’s Beginning mail-order catalog company. The company currently employs 20 operators who are paid $10 per hour in wages and benefits and can each handle an average of six calls per hour. Assume that interarrival times and service times follow the exponential distribution. A maximum of 20 calls can be placed on hold when all the operators are busy. The company estimates that it costs $25 in lost sales whenever a customer calls and receives a busy signal.
a. On average, how many customers are waiting on hold at any point in time?
b. What is the probability that a customer will receive a busy signal?
c. If the number of operators plus the number of calls placed on hold cannot exceed 40, how many operators should the company employ?
d. If the company implements your answer to part c, on average, how many customers will be waiting on hold at any point in time and what is the probability that a customer will receive a busy signal?