Company S currently has three counters, each staffed by a single employee, and a single first-come-first-serve queue for all customers to join. You think that the current system is wrong. You would like to redesign the queues so that there is a dedicated queue and a dedicated server for each customer type (type 1, type 2, and type 3). No customers cross between servers.

Type 1 clients arrive at a rate of 19 per hour.

Type 2 clients arrive at a rate of 15 per hour.

Type 3 clients arrive at a rate of 6 per hour.

Each of the three serving employees takes an average of 3 minutes to complete a transaction.

Assume inter-arrival and service times follow an exponential distribution.

Find the average inventory in service in the existing system.

Find the average service time (in minutes) in the existing system

Find the total time (in minutes) in the new system for the type 2 clients

Find the average wait time (in minutes) in the existing system. Round your final answer to four decimal places.

Find the average wait time (in minutes) in the new system for type 2 clients.