What more do you need? It won't let me put in all of the fluff. The total time it takes between when you arrive at the restaurant until you leave is made up of the following elements:

The service time for the CSM to process your order

The service time for the FPM to prepare your order

The waiting while the CSM and FPM served other customers

To model this using the queuing models in the chapter, assume that you have two totally independent service processes. The first process is the CSM and the second is the FPM$.$Each process has potentially a different mean service time per customer. The CSM must serve each customer and they arrive at a particular rate. The FPM prepares the individual items on the order such as hamburgers, cheeseburgers, and fries. As the orders are taken, each individual item appears on a monitor telling the FPM what should be made next. The average time for a customer to run through the system is the sum of the average service times $($time to take the order by the CSM and time to make the order by the FPM$)$plus the sum of the expected waiting times for the two processes. This assumes that these processes operate totally independent of each other, which might not be exactly true. But we leave that to a later discussion.

Assume that the queues in front of each process are large, meaning that there is plenty of room for cars in the line before and after the order kiosk. Also, assume there is a single CSM and two FPMs each operating independently and working just on the drive$-$through orders. Also, assume that the arrival pattern is Poisson, customers are handled first come, first served, and the service pattern is exponential.

Consider a base case where a customer arrives every $37$seconds and the Customer Service Manager can handle $138$customers per hour. There are two Food Preparation Managers, each capable of handling $94$orders per hour. Use Exhibit$\_10\mathrm{.}9.$

If the restaurant runs a sale and the customer arrival rate increases by $15\%,$calculate the total time expected to serve a customer.

Note: Do not round intermediate calculations. Round $"$Lq$"$value and final answer to $4$decimal places.

Calculate the average number of cars in the drive$-$through line.

Note: Do not round intermediate calculations. Round $"$Lq$"$value and final answer to $4$decimal places.