A theme park has partitioned customers into two classes for check-in purposes. Instead of splitting the line into two M/M/1 queues (one for each respective type), they have decided on a layout consisting of one "priority" M/M/1 queue with a capacity of u = 60 customers per hour. The arrival rates have been, on average, y = 12 per hour for type-one (priority) customers, and 12 = 36 per hour for (general) type-two customers. 18. Type-one customers go through the system with no interruptions (that is, they are treated as if they were the only ones there and E(L1) = P1/(1 - 1) is in familiar form). What is the average time (seconds) a type-one customer spends in the system? 19. Given the interruptions of type-two customers by type-ones, we have to modify the formula reflecting the mean number in the system as follows: E [L] P2 (1 - 1) (1 - P1 - P2) Considering the above derivation, what is mean number of type-two customers in the M/M/1 priority system? 20. How much faster is a type-one customer's overall service that is, time spent in the system) in seconds than a type-two customer