Develop a simple checkout system. That system was so successful that they've decided to expand their operations by opening additional checkout lanes. Unfortunately, they are unsure of just how many lanes they need to add. Ideally, Cougar Mart would add enough lanes to satisfy expected demand. However, opening too many lanes would mean that they're paying checkers to staff empty lanes. Your goal is to develop a checkout lane simulation that can be used to determine the optimal number of lanes that Cougar Mart should have open.

Your program should simulate an entire day at Cougar Mart, in minutes. For this simulation, we will assume that Cougar Mart is open 12 hours a day. As this is a simulation, you don't actually need to run your program for 12 hours. Instead, consider the time span to be an integer, with each minute being a number. As such, 0 would indicate the start of the simulation, 1 would represent the first minute of the simulation, 2 the second minute, and so on.

Program Flow

Your simulation should operate as follows:

1. Prompt the user for the number of checkstands to simulate

2. Create a vector that contains the appropriate number of checkstands

3. Set the probability of a new customer arriving equal to 0.

4. For each minute in the simulation

a. Determine if a new customer has arrived.
i. Generate a random number between 0 and 5.
ii. If the random number is less than or equal to the probability of a new customer arriving (Step #3), go to Step 4.B.
iii. If the number is greater than the probability of a new customer arriving (Step #3), increment the probability of the new customer arriving by 1. Go to Step 4.C.

b. If a new customer has arrived, create a new customer whose arrival time is equal to the current simulation time and whose service time is a randomly generated number between 1 and 4. Next, try to find an empty checkstand. If one exists, place the customer in the line at that checkstand. If no empty checkstand exists, randomly select a checkstand for the customer to enter.

c. For each checkstand in the simulation:
i. If there is at least one customer in the checkstand, go to 4.C.II. Otherwise, go back to 4.C.
ii. If the first customer in line has not received a departure time, calculate one. Departure time = arrival time + service time.
iii. If the total time elapsed is greater than the first customer's departure time, then the customer has completed the checkout process. Remove them from the queue.
d. Increment the elapsed time in the simulation

5. After the simulation completes, write the results to a CSV file in the following format:

, , , , , .

Also include the total number of customers generated during the simulation at the top of the CSV file. Note that an example CSV file will be included with this assignment description. I have provided a CsvWriter class to aid in the construction of CSV files.