The following information is given about a 24-hour car wash facility: • There are 2 car washes 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 vehicle washing time follows the exponential distribution and its average is 12 minutes. • 30 TL is charged as a washing service fee for 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 has said that if it wants, it can rent the parking lot to the car wash facility 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, a maximum of 5 vehicles will be available at the same time. Should the facility lease this parking space from the municipality? Solve it by showing the necessary operations and writing their explanations.
The following information is given about a 24-hour car wash facility: • There are 2 car washes 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 vehicle washing time follows the exponential distribution and its average is 12 minutes. • 30 TL is charged as a washing service fee for 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 has said that if it wants, it can rent the parking lot to the car wash facility 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, a maximum of 5 vehicles will be available at the same time. Should the facility lease this parking space from the municipality? Solve it by showing the necessary operations and writing their explanations.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The following information is given about a 24-hour car wash facility: • There are 2 car washes 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 vehicle washing time follows the exponential distribution and its average is 12 minutes. • 30 TL is charged as a washing service fee for 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 has said that if it wants, it can rent the parking lot to the car wash facility 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, a maximum of 5 vehicles will be available at the same time. Should the facility lease this parking space from the municipality? Solve it by showing the necessary operations and writing their explanations.
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