Problem 3. (36 points) Managing and Estimating Delays. AUzons customer call center schedules 12 call agents between 1pm and 2pm to answer customer calls. On average, it takes 12 minutes to handle a call on the average with standard deviation of 10 minutes. Calls come in every 1.1 minute on average with a standard deviation of 1.5 minutes during this period.

a) (5 points) What is the capacity of the call center for this period in calls per hour?

b) (5 points) What is the minimum number of call agents to strictly handle the demand for this period? Show your work!

c) (6 points) What is the average time a customer spends in the system in minutes?

d) (6 points) What is the average total number of customers at the call center either waiting or talking to call agent?

e) (6 points) What is the probability that the customer call center is idle?

f) (8 points) At most, how many call agents should be scheduled for this period to keep the utilization of the call center at least at 70%?

NOTE: SHOW ALL YOUR WORK. USE 4 DECIMAL PLACES IN ALL CALCULATIONS.