Tech has a student population of 30,000 and is located in a small college town in Virginia. DirectCast Cable TV has a small service staff or three installation trucks and technicians that is sufficient to handle service calls and installations for almost the entire year. However, for the month-long period right before and during the beginning of fall semester in August, when all the students return, the cable TV service is overwhelmed. During the normal year DirectCast averages about 15 service requests per day (Poisson distributed), and service calls average about 50 minutes (exponentially distributed) during their 8-hour workday. However, during the month before school starts, the demand for service calls triples, and almost all of these are requests for installations, so the average service time increases to 80 minutes. During normal demand periods, DirectCast guarantees service within a 24-hour period.
a. What will the cable service and customer waiting time be like during the month before the semester starts?
b. It is possible for DirectCast to “borrow” trucks and crews from other company offices. How many extra trucks would it need to provide its normal service guarantee?