Beta Innovation Center, BIC, operates a technical support center for its software clients. Now BIC has new software, security protection system. However, the clients are not familiar with the implementation. If the clients have installation and encounter problems with security protection system, they may telephone the technical support center and obtain the consultation. Currently, BIC employs four staffs to give the consultation to the clients who call to contact the center. If all staffs are busy when the client call arrives, the client will hear the recorded voices stating that all staffs are serving the other clients. The call of the first client in waiting line will be connected to any staff who is first available. The client calls are distributed with Poisson distribution, with an average of 10 calls per hour. On average, it takes 12 minutes for the staff to answer the questions for each client. The service time follows an exponential distribution.

3.1) In the current system, What is the probability that there is no client in the system

3.2) On average, how many clients are there in the technical support system? On average, how long does it take for each client to wait before start talking to the staff?

3.3) What is the probability that a client willhave to wait before start talking to a staff?

3.4) Staffs at CIC are paid 250 baht per hour and there is opportunity cost of 350 baht per hour for a client when he/she must wait in the waiting line. Determine the total cost of this system.

3.5) The customer service department recently receives several letter from the clients complaining about the difficulty to get the service. The service manager and the process manager agree to improve the service. After collecting historical information, 40 percent of clients who would like to ask about the installation. The service time is 15 minutes in average and standard deviation is 4 minutes.The service time follows general distribution. BIC arranges the new telephone number for these clients and assigns one of four staffsto serve the "Installation Line" for these clients. The rest of the clients would ask about the troubles in using the software which takes 10 minutes and follows exponential distribution. Theremaining staffs will take careof these clients with the current telephone system and rename the service line as "The Trouble Shooting Line". In other words, the system has 3 staffs and there is only 1 waiting line for this "Trouble Shooting Line". On Average, what is thetotalnumber of clients in the new system?

3.6) Compare the current system (from question 3.4) and the new system (from question 3.5) using the total cost. Should the manager switch the operation to the new system? (4 points)