This is a stochastic modeling question, please solve it that way.

The following information is given about a 24-hour car wash facility:

There are 2 car wash machines and a waiting area for 2 cars in the car wash facility. Thus, while maximum 2 vehicles can be washed in the facility at the same time, maximum 4 vehicles can be found in the facility.

The number of vehicles arriving at the facility conforms to the poisson distribution, with an average of 6 vehicles per hour. The car wash time, on the other hand, follows the exponential distribution and its average is 12 minutes.

30 TL is charged for washing service from each vehicle, and the cost of washing is 10 TL per vehicle.

There is a parking lot for 1 vehicle belonging to the municipality right next to the car wash facility. The municipality claimed that the car wash facility can rent the parking lot for 100 TL per day. If this parking lot is rented, the capacity of the waiting area will be 3 vehicles, and when the washed vehicles are included, there will be a maximum of 5 vehicles at the same time.

Should the facility rent this parking space from the municipality? Solve it by showing the necessary operations and writing their explanations.