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3. (20 points) At Shorter Beach Airport, all passengers have to go through two security check points before arriving at the gate. A typical passenger's experience is as follows: Security Check point 1 There is only one TSA officer at Security Check Point 1. A passenger presents her ID and boarding pass to the TSA officer. The TSA officer checks the ID and puts a stamp on the boarding pass. It takes 60 seconds on average for the officer to process one passenger, and service (process) times are exponentially distributed. Passengers arrive according to a Poisson process. To go through Security Check Point 1 on average takes 4 minutes (This includes waiting time and process time). Security Check point 2 Then each passenger has to take the automated X-ray machine,' It takes 2 minutes on average to scan (process) one passenger. There is only one X-ray scanner at Security Check point 2. The airport administration estimates that on average there are 6 passengers at Security Check Point 2 (Thi includes those who are waiting in line and those who are being scanned). a. (6 points) What is the utilization of the TSA officer at Security Check point 1 ? U=.75 b. (4 points) What is the arrival rate (or flow rate) at Security Check point 1 ? .75 passenger/min or 45 passengers/hour c. (4 points) How many passengers are there on average at Security Check Point 1, including those who are being checked by the TSA officer and those who are waiting to be checked? d. (3 points) How long does it take a customer to go through Security Check point 2 , including the waiting time and process time? 8 mins e. (3 points) On average, how long does it take a passenger to arrive at the gate (How long does it take a passenger to go through the two security check points?) 12 mins