Cars stay in the parking lot for an average of $30$ minutes, and the parking lot can have at most $30$ cars.

There are $5$ workers in the pre$-$wash station, each can handle a prewash service in $4$ minutes per car. $60\%$

of all cars want standard cleaning service and $40\%$ of all cars want deluxe cleaning service. Standard

cleaning takes $4$ minutes for a standard cleaning machine and Deluxe cleaning takes $10$ minutes for a

deluxe cleaning machine. All cars complete the service by going through the drying station. There are $4$

workers in the drying station, each can handle a drying service in $10$ minutes per car.