$**$PLEASE USE THE Queueing Model ON EXCEL TO ANSWER THIS QUESTION.$**$

The manager of the call center of a large airline company needs to determine the optimal number of

operators that she should hire. The call center serves two types of clients: Business $($B$)$ and Leisure $($L$)$

customers. She has determined that B calls arrive according to a Poisson process at a rate of $20$ calls

per hour. On the other hand, $L$ calls arrive according to a Poisson process at a rate of $60$ calls per hour.

Two types of operators are available on the market: High skill $(H)$ and Average skill $($A$),$ which differ on

their ability and speed to serve both types of clients. $H$ operators can serve both types of customers

and the average amount of time that they need is $10$ minutes per call independent of the type. On the

other hand, A operators can serve only L calls and they need on average $15$ minutes per call. Assume

that all service times are exponentially distributed.

The cost of hiring an $H$ operator is $$28$ per hour while the cost of hiring an A operators is $$18$ per hour.

The manager has also estimated that the cost of keeping a B customer waiting in queue is $$50$ per

customer per hour while the cost of keeping an L customer waiting in queue is $$5$ per customer per

hour.

The manager is considering two possible configurations:

Configuration $1$: Single queue

Have a single queue for both type of calls and hire only $H$ operators that will serve both types of calls.

Calls will be served on a First$-$Come$-$First$-$Serve base independent of their type.

Configuration $2$: Two separate queues

Have two separate queues, one for each type of calls. For the B calls queue, she will naturally hire only

$H$ operators. For the $L$ calls queue, she can either hire $H$ operators or A operators. However, she does

not want to mix $H$ and A operators. So she has to decide which one of the two types of operators to

use.

$1)$ If the manager chooses configuration $1,$ what is the optimal number of $H$ operators that she

should hire?

$2)$ If she goes for configuration $2,$ which type of operators should she use for the $L$ calls queue?

$3)$ Which one of the two alternatives do you recommend? What is the optimal staffing in this

case?

Please show all your work. Explain carefully your approach.