It is the tax season. Altas Tax Inc. is planning to open an office inside of the Pacific Mall. On average, it is estimated that the customers arrive at the store every 20 mins. Arrivals follow a Poisson distribution. Assume customers always form one common line when arriving at the store. There are 3 plans available - the manager needs to decide which plan to use for this new office. Plan 1 is to use a self-serve tax filling machine, which can serve customers' requests in exactly 15 mins. Plan 2 is to hire 2 junior accountants. On average, each can serve 3 customers per hour with the service time following an exponential distribution. Plan 3 is to hire one senior accountant. The time to serve a customer has a mean of 12 minutes and a variance of 36 minutes. Q1. What is the Kendall notation for Plan 1, Plan 2, and Plan 3? Q2. For Plan 1, what is the average number of customers waiting for the service? Q3. For Plan 2, how long does a customer need to wait before being served? (in minutes) Q4. For Plan 3, what is the total number of customers in the system? Q5. Which plan has the lowest utilization? Q6. If the manager wants to choose the plan with the lowest probability that zero customers are waiting, which plan should be chosen? Q7. If the manager wants to choose the plan with the shortest time to spend in total for the tax filing service, which plan should be chosen?