Course code & title : MS5225 System Modeling and Simulation

Session : Semester B 2008/09

Time allowed : Three hours

This paper has THREE pages (including this cover page).

1. This paper consists of 2 questions.

2. Answer BOTH questions.

3. You do not need to write your solutions on answer books. All the answers should be (1) Uploaded to the blackboard and (2) Emailed to

IMPORTANT NOTES: after the examination, you will be given 5 minutes additionally for uploading your solutions to blackboard. For safety, you are encouraged to also email a copy to yanzhili@cityu.edu.hk.

Question 1: (20 marks)

Tort Motors is considering whether to introduce a new model called the Racer. The profitability of the Racer will depend on the following factors:

a. Fixed cost of developing the Racer: Fixed cost is equally likely to be $3 or $5 billion.

b. Sales: Assume that year 1 sales will be normally distributed with mean 200,000 and standard deviation 50,000. Then assume that year 2 sales are normally distributed with mean equal to the actual year 1 sales and standard deviation 50,000 and that year 3 sales are normally distributed with mean equal to the actual year 2 sales and standard deviation 50,000.

c. Price: Assume year 1 price is $13,000. Then the year 2 price will be

1.05 * (year 1 price + $30 * % diff1)

where % diff1 is the percentage by which actual year 1 sales differ from expected year 1 sales. The 1.05 factor accounts for inflation. For example, if the actual year 1 sales figure is 180,000, which is 10% below the expected year 1 sales, then the year 2 price will be

1.05 * [13,000 + 30 * (-10)] = $13,335

Similarly, the year 3 price will be 1.05 * (year 2 price + $30 * % diff2) where % diff 2 is