A wireless phone carrier has a retail store at the local Mall, which is in charge of Sales for new services and maintenance and assistance to existing account a holder. Arrivals to the store are Poisson with an average rate of 6 customers per hour. Approximately, 80% of the arrivals are Sales related and the rest are Maintenance of the existing account holders. Customers join a queue and are served on a First-Come-First-Served basis. Currently, the store has one agent who handles all customers (sales and maintenance of existing accounts). The time an agent spends with a customer is exponentially distributed with a mean of 6 minutes. A detailed study shows that around 40% of the potential new sales customers decide to get the wireless service (the rest leave the store after talking to the agent). The carrier pays those customers who open a new account $100 if they wait more than 2 minutes in line.
a) Identify the queuing system associated with the operation and find the average total hourly cost of the queue operation.
b) Management is considering the creation of two separate lines, one for each of the customer types (sales and maintenance). In this configuration, the service times for each queue will remain as before (exponential with a mean of 6 minutes) but an additional agent must be hired. To make this two-line configuration more cost-effective (lower average total cost) than the original configuration, what is the maximum wage ($/hour) to pay the additional agent. (Show all your work)