Problem
Mark Zickenberg is an engineer in a social media company. He responds to a variety of complaints from customer's regarding the company's algorithms. He receives a complaint every 40 minutes to his email inbox. It takes him an average of 30 minutes to respond to these complaints. Mark believes that adding a second engineer would significantly improve his department's efficiency. He has a friend, Elon Musty, who is looking for a job. He estimates that adding an assistant, but keeping the department running as a single-server system, would allow complaints to be responded to in half the time, an average of 15 minutes to respond to these complaints.
The engineers earn $950 per hour (they are a bit overpaid) while the company, due to loss of goodwill, estimates it lose $750 in advertising per hour because customers are waiting to get their problems resolved.
I. Consider the performance of the office before the new engineer is added. On average, how many complaints (to the nearest 0.01 complaint) are in the system given the arrival and service rates?
II. Consider the performance of the office before the new engineer is added. On average, how many hours (to the nearest 0.01 hour) does each complaint spend in the system given the arrival and service rates?
III. Consider the performance of the department before the new engineer is added. Based on the average number of complaints in the system, what is the total system cost (per hour (to the nearest $/hour)?
IV. Consider the performance of the office after the new engineer is added. On average, how many complaints (to the nearest 0.01 complaint) are in the system given the arrival and service rates?
V. Consider the performance of the office after the new engineer is added. On average, how many hours (to the nearest 0.01 hour) does each complaint spend in the system given the arrival and service rates?
VI. Consider the performance of the office after the new engineer is added. Based on the average number of complaints in the system, what is the total system cost per hour (to the nearest 0.01 $/hour)?
VII. Based on your cost analysis - is it worth it to add another engineer?