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Each question has the answer and I just need to see the steps to get that answer

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 ofcer at Security Check Point 1. A passenger presents her ID and boarding pass to the TSA ofcer. The TSA ofcer checks the ID and puts a stamp on the boarding pass. It takes 60 seconds on average for the ofcer 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.1 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 (This includes those who are waiting in line and those who are being scanned). a. (4 points) What is the utilization of the TSA officer at Security Check point 1? U=3/4. b. (4 points) What is the arrival rate (or flow rate) at Security Check point 1? 3l4 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 ofcer and those who are waiting to be checked? W|P=3 d. (4 points) How long does it take a customer to go through Security Check point 2, including the waiting time and process time? 8mins. e. (4 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 minutes. 1 The machine is so technologically advanced that no TSA ofcers need to be at Security Check Point 2. 4 USC Marshall School of Business BUAD 311 Operations Management Spring 2023 (20 points) Inner City Adventure is one of the many projects of USC Marshall's Brittingham Social Enterprise Lab. Construction of the amusement park just east of downtown Los Angeles is complete except for the restaurant. You are hired by the project as process consultant. (You work pro bono of course) According to the current business proposal, a typical park guest's experience will be as follows: A guest comes to the park gate to purchase a ticket. There are three ticket agents each of whom can sell a ticket to a guest in 30 seconds on average.2 It takes 2 minutes on average to get a ticket (wait time = 1 min 30 sec and process time = 30 sec). Because of the small size of the park, there are only two attractions in the park \"It's a Tiny World" and \"Galactic Magnum Mountain.\" \"It's a Tiny World" takes exactly 4 minutes, and 40 guests can enjoy the ride at one time.3 Before a typical guest can enjoy \"It's a Tiny World," she has to wait 8 minutes on average in line. The other attraction \"Galactic Magnum Mountain" takes exactly 3 minutes, and 15 guests can enjoy the ride at one time. There are, on average, 15 guests here, including those guests waiting and those who are enjoying the ride. Because of the awkward land, the park is designed such that each guest enjoys only one of the two attractions. After enjoying a ride, some guests go to the restaurant to try the famous European gourmet sausages while others who are not hungry leave the park without eating. After market survey, the project team learns that 90 guests per hour will come to the theme park, a half of whom will enjoy \"It's a Tiny World\" and the other half \"Galactic Magnum Mountain." The survey also nds that only 5% of the guests who enjoy \"It's a Tiny World\" will dine at the restaurant while 15% of those who enjoy \"Galactic Magnum Mountain" will. Those who eat will spend 30 minutes in the restaurant, that is, FT = 30 minutes including waiting time and eating time. Now the project team has to decide how many seats they should have in the restaurant. The current construction plan indicates that they will have 20 seats. a. (4 points) How many guests are there on average at the ticket counter, including those who are waiting and those who are buying tickets? 3 guests 2 For simplicity, assume all the guests are \"solo.\" No guests come in groups. 3 Again, for simplicity, assume that loading and unloading of guests take no time. 5 b. (4 points) How many guests are there at "It's a Tiny World," including those who are waiting before the ride and those who are enjoying the ride? 9 guests c. (4 points) What is the flow time for "Galactic Magnum Mountain," including the wait time and the 3-minute ride duration? 20 minutes d. (4 points) What is the flow rate at the restaurant? 9 guests/hour e. (4 points) How long do guests spend on average at the theme park (overall flow time)? 21 minutes