The computer lab at State University has a help desk to assist students working on computer spreadsheet assignments. The students patiently form a single line in front of the desk to wait for help. Students are served based on a rst-come, rst-served priority rule. Students arrive at the help desk at the rate of 4 every 10 minutes. The average service time is 2 minutes. The Poisson distribution is appropriate for the arrival rate and service times are exponentially distributed.

a) What is the average time a student is in the lab?

b) What is the average number of students in the lab?

c) What is the average number of students waiting to receive service?

d) What is the average time a student is in the queue?

e) What is the probability that there are no students at the computer lab?

f) What percentage of the time is the help desk busy?

g) What is the probability that there are exactly 2 students in the lab?

h) By how much would your answer to part (a) be reduced if a second help desk, which could do the same work, were added?

Question 8.2

A fabric factory has 5 weaving machines in use. These weaving machines need repair after about 20 hours of use. Breakdowns have been determined to be Poisson distributed. Jim, the maintenance worker can service a weaving machine in an average of 2 hours, following an exponential distribution. Weaving machine downtime costs $120 per hour. Jim is paid $25 per hour.

a) What is the average time a weaving machine is waiting to be repaired?

b) What is the average number of weaving machines in the repairing area?

c) What is the total hourly costs?

Question 8.3

William's Window Hardware is looking for a new supplier for its casement window operators. William consider price and reputation as the most important criteria. He considers reputation to be four times more important than price. William has narrowed his choices to two suppliers. On a 10-point scale, he has assigned Rideau's Windows Supply a score of 9 on price and 4 on reputation. He has assigned Ian and Family a score of 3 on price and 6 on reputation. Apply the factor weighting technique to help William choose a new window operator supplier.