Sample Paper 6 Final exam questions updated PDF

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Question 2During lunch time from 12:00 noon to 1:30pm, a train runs from station A to station B at the interval of 5 minutes. The train only has 1 cabinet and it can accommodate 100 people. When people arrive at station A, they will queue in a line and when the train arrives, they will board the tra...

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Question 2 During lunch time from 12:00 noon to 1:30pm, a train runs from station A to station B at the interval of 5 minutes. The train only has 1 cabinet and it can accommodate 100 people. When people arrive at station A, they will queue in a line and when the train arrives, they will board the train based on first-come-first-served. Each ticket costs $1.2. Based on the past history, people arrive at the station during 5 minutes interval follows the distribution.

Probability 20% 50% 20% 10%

Number of people arriving in 5 minutes interval 80 120 150 180

Follow the template below, each row in the template starting from row 6 represents a train arrival time (Column B), number of passengers arrived before the train arrival at the station (Column C), total passengers at the station who are ready to board the train (new arrival plus the previous row remaining passengers in the queue) (Column D), number of people who can board the train (Column E), # of people remaining in the queue after the train left due to train capacity (Column F) (those people who can’t board the train) will remain in queue until the next train arrives and finally maximum number of trains people in the queue in Colum F need to wait (Column G), Revenue (Column H).

(a)

Using the Excel worksheet template given above, write down the key formulas for the following. Each row in the worksheet from (A6: A24) represents a train arrival. Ensure that you can fill your formula within the same column. You may use any addition column to generate the demand. (3 marks) Pax arrived before the train arrived (C6) Pax at station A (D6)

Pax on train (E6)

No. of pax remaining in Queue after train left (F6) Max # of trains the people in the queue need to wait (G6) Revenue (H6)

(b) Simulate 10 times to determine the average pax. at station and average number of pax. in queue and average revenue during the lunch time. (2.5 marks) Description Average total number of passengers arrived at the station Standard deviation of total number of passengers arrived at the station

Answer

Average total number of passengers in the queue at each 5 minute interval

Maximum duration that pax. In the queue needs to wait

Average total revenue during lunch time

(c)

The management would like to find out the impact of train capacity on the number of people queuing at the station. Perform “what-if” analysis to identify the average number of pax. in queue if we vary the train capacity from 90, 110 and 120, get an average of 10 simulation. (2 marks)

Train capacity

Average # of pax. in queue

90 110 120

The minimum number of train capacity: _______________________ if we want the average queue length at the station to be less than 150. (Hints: you may make use of the result above. !

(d)

The train operator realize that there are too many passengers waiting at the station and they should limit the number of people at the station (new arrival plus those already in the queue) to be 200 at any one time. The passenger who arrives after 200 will be rejected. Develop a model to compute the new revenue each day based on the current train capacity of 100 and station capacity of 200. Include two columns I and J to the left of the original

model to compute the number of rejected passenger and new revenue based on station capacity. (2.5 marks)

Based on the new model, write down the key formulas for the following: Number of people rejected (I6) Number of people in Queue (F6) New Revenue (J6)

Simulate 10 times, new average revenue per day is: _____________________________

(e)

This question is independent of the previous 4 part. The train operators intend to buy some new trains with bigger capacity which can accommodate up to 150 and average daily passenger during lunch time is 2500 passengers, and the new investment cost is 5 million dollars. The company is also going to increase the ticket price by 10% each year from previous year and current ticket price is $1.20. Assume that there are 365 days in a year, the revenue is solely from lunch time train and 50% of the revenues go to other operational cost. Compute the yearly profit/ (Return) for the next 10 years and fill in the value in the table below under investment or return column. Compute the net present value for the investment for the years indicated (Year 0, 1,2, 8 and 9). What is the minimum number of years required for the company to have a positive return from the investment, taken into consideration of 8% discounted rate annually? (3 marks)

Year 0 1 2 8 9

Investment/Return

Net Present Value

-$5,000,000

-$5,000,000

Minimum years required to have positive return:

Net present value after 10 years of investment is:...