TechSoft Systems operates a technical support center for its software customers. If customers have installation or use problems with TechSoft software products, they may telephone the technical support center and obtain free consultation.

Currently, TechSoft operates its support center with one consultant. If the consultant is busy when a new customer call arrives, the customer hears a recorded message stating that all consultants are currently busy with other customers. The customer is then asked to hold and is told that a consultant will provide assistance as soon as possible.

The customer calls follow a Poisson probability distribution, with an arrival rate of five calls per hour. On average, it takes 7.5 minutes for a consultant to answer a customer's questions. The service time follows an exponential probability distribution.

TechSoft's customer service department recently received several letters from customers complaining about the difficulty in obtaining technical support. If TechSoft's customer service guidelines state that no more than 35% of all customers should have to wait for technical support and that the average waiting time should be two minutes or less, does your waiting line analysis indicate that TechSoft is or is not meeting its customer service guidelines? What action, if any, would you recommend?

You need to determine the information for the case of one server (in the case of multiple servers, you are provided with these results in the table).

Fill in the blanks in the table. (round to two decimals)

Fill in the blanks in the table. (round to two decimals) Measurements Number of servers One Two Three Probability of: Zero callers 0.52 0.53 Probability of: One caller 0.33 0.33 Probability of: Two callers 0.15 0.10 0.10 Probability of: Four callers 0.06 0.01 0.01 Utilization 0.31 0.21 Average number of callers waiting in line 0.07 0.01 Average waiting time in line in minutes 0.81 0.09 Average number of callers in the system 0.69 0.63 Average time in the system in minutes 8.31 7.59In addition, answer following. What is the probability of being served immediately when the number of servers is: a. one server b. two servers c. three servers a. What staffing level meets the goal set by top management? b. What staffing level do you recommend and why? c. For your recommendation: i. What percent of customers will be served immediately? ii. What is the average waiting time in line? iii. What percent of the time will the servers be busy on average