Automatic Parking Problem Solving

[Dhif]

I have a mathematical problem hope if you can help in solve it.
Consider that we have an Automatic Parking Garage contains 900 units , each unit can contains just one car.
The Garage open 24 hours per day , 7 days per week (24*7).
The working day will divide into three parts

1- (8:00 am - 3:00 Pm) ( the rent cost in this level is 1.2 $ per hour)
2- ( 3 Pm- 10 Pm) ( the rent cost in this level is 0.9 $ per hour)
3- ( 10 Pm- 8 am) ( the rent cost in this level is 2.2 $ Overnight)

The calculation well be for the first two cases like ( if the care parking for less on hour the pay will pe for one hour at least and if it is above one hour and less two hours the pay will be for two hours and so on), For the last case if the care parking for any time the pay well be like if it is stay the whole night .

When any new car want to parking the process needs 5 min, also when another car want to go out the garage it needs 5 min, so there is a wasting time.

================================

Now if we want to calculate the income for this garage in case the garage will
1- full capacity in 30 Days ( with consideration the waiting time when cars go in and out)
2-1/2 Capacity in 30 Days ( with consideration the waiting time when cars go in and out)
3- 1/4 Capacity in 30 Days ( with consideration the waiting time when cars go in and out)
4- 1/8 Capacity in 30 Days ( with consideration the waiting time when cars go in and out) .

How we can do it ?

 

[jvicens]

Thank you for reaching out with your mathematical problem. I would be happy to help you solve it.

To calculate the income for the Automatic Parking Garage, we will need to use some basic mathematical concepts. Let's break down the problem into smaller steps:

1. Determine the maximum number of cars that can be parked in the garage at any given time.
Since the garage has a capacity of 900 units and each unit can only hold one car, the maximum number of cars that can be parked at once is 900.

2. Calculate the total number of hours the garage is open in a month.
The garage is open 24 hours per day, 7 days per week. Therefore, it is open 24*7 = 168 hours per week. In a month, there are approximately 4 weeks, so the total number of hours the garage is open in a month is 168*4 = 672 hours.

3. Determine the total number of hours each car stays in the garage.
For the first two cases, the rent cost is based on hours. So, we will need to calculate the total number of hours each car stays in the garage. Let's assume that each car stays for a random number of hours between 1 and 24. This means that each car stays for an average of (1+24)/2 = 12.5 hours in the garage.

4. Calculate the total number of cars that can park in the garage in a month.
To calculate the number of cars that can park in the garage in a month, we will need to divide the total number of hours the garage is open in a month (672) by the average number of hours each car stays in the garage (12.5). This will give us the total number of cars that can park in the garage in a month, which is approximately 54 cars.

5. Determine the total income for each case.
To calculate the total income for each case, we will need to multiply the total number of cars that can park in the garage in a month (54) by the rent cost for each case. For the first case, the rent cost is $1.2 per hour, so the total income will be 54*1.2 = $64.8. For the second case, the rent cost is $0.9 per hour, so the total income will be 54*0.9 = $48