Quality Business Services (QBS) receives a wide variety of customer emails. Messages range from requests for technical support from existing customers to general inquires about products from potential customers. QBS's policy is to reply to all emails within 24 hours of receipt. QBS has two contact centers processing emails. The first is on the east coast (NY) and is open from 8:00AM to 4:00PM (all times are Eastern Standard Times). It can process 450 emails per hour. The second facility is on the west coast (LA) and opens at noon (EST) and can process 300 emails per hour. It also operates for an eight-hour shift. The two contact centers pull emails from the same server in a first come, first served fashion. Work unfinished by the east coast facility is completed by the west coast center. On an average day, emails arrive at a rate of 350 per hour from 8:00AM until 6:00PM (EST). At all other times, emails arrive at a rate of 150 per hour.

QBS plans to close one facility and increase the staffing at the remaining facility so that it can handle 700 emails per hour during the same original 8 operating hours.

1. Using the new single facility plan, will QBS still be able to answer all emails arriving within a 24-hour period?

2. What is the longest time that a customer will have to wait for a reply in the old and new systems?

3. Does it matter which center is closed? Which would you close and why?

4. Would you switch to the new system with your closing recommendation in c)? or stay with the old system. Explain your reasoning

5. How do the answers to a) and c) change if emails arrive not at a constant rate but at a rate that is Normally distributed at N(350,150) and N(150,45) i.e. with the same means as before but with a standard deviation.