Quantitative methods exam questions and answers pdf

Project Management Programme PMGT 6867 Quantitative Methods in Project Management Time Allowed: 2 Hours Total Marks: 60 Instructions to Candidates 1. The paper comprises of 4 question sets, each with several parts. Answer all four questions. You have to answer in separate answer script that will be provided. 2. This is closed book exam. 3. The mark to be awarded for each part is indicated. 4. Write your final answers in ink. 5. Only electronic calculators are permitted to use in this examination. Question Set: 1 (a) What are the advantages and disadvantages of Return on Investment (ROI)? (1+1=2 marks) (b) Distinguish Net Present Value (NPV) and Economic Value Add (EVA). (1 mark) (c) Cash flows of two projects (i.e., Project A and Project B) are as follows. Years 0 1 2 3 4 Project A - 11,000 5,000 1,500 4,000 1,000 Project B -12,000 6,000 5,000 3,000 2,000 Calculate the Payback Period for these two projects. (2 marks) (d) Sydney Builder (a construction company) is considering building either a one-storey (Project A) or five-storey (Project B) block of offices on a prime site. Both projects have oneyear duration. The following information is available: Initial Investment Outlay Net Inflow at the Year End Project A -9,500 11,500 Project B -15,000 18,000 In terms of Net Present Value (NPV), which project is better or more acceptable? (Assume that discount rate is 10%). (2 marks) In terms of Internal Rate of Return (IRR), which project should Sydney Builder undertake? (2 marks) (e) A company is planning to produce 1,000 bicycles in next 2 years (each year 500). The fixed cost is $100,000. The variable cost for each bicycle is $100 and $120 for the first and the second year respectively. The unit selling price is $200 (same for the first and the second year). (i) Does the company make a profit or loss? (2 marks) (ii) What should be break-even selling price for each bicycle if the company produces 500 bicycles in 1st year and 500 in the second year? (2 marks) (iii) How many bicycles that company needs to sell at break-even point if the selling price is $200 per bicycle? (2 marks) Question Set: 2 (a) What is PERT and CPM? In a project, for a task (say updating a computer software to comply with the new system), the following information is given: Optimistic (time) = 3 days, Pessimistic (time) = 6 days, and Most likely (time) = 4 days). Find out PERT for this task. (2+1=3 marks) (b) Illustrate the difference between Lead Time and Lag Time with example. (2 marks) (c) The table below describes activities needed for a given project. # Description Duration(Hours) Predecessors A Design Search form 1 - B Learn some PHP 2 - C Draft PHP 1 B D Alpha test 1 A,C E Improve form 4 D F Improve PHP 2 D G Beta test 1 E,F H Release 1.0 1 G I Learn PHP RegExs 2 B J Update PHP 2 H,I K Update form & test 1 J - Release 2.0 (Finish) - K Find out the Critical Path for this project. Also find out potential Near Critical Path. (3 + 1 = 4 marks) (d) You have 20 marbles: 4 red and 16 blue. You take one of them randomly and do not put it back. Then you take a second marble randomly. Two events are defined as follows: A {the 1st marble is red} and B {the 2nd marble is blue}. What is the probability that first marble is red and the second marble is blue, i.e., P (A ∩ B)? (2 marks) (e) Draw a probability tree for a coin which has been flipped three times. (1 mark) Also, find out the probability of the following outcomes from this probability tree: (i) P(exactly two tails) (1 mark) (ii) P(exactly one head and more than one tail) (1 mark) (iii)P(more than or equal to one head) (1 mark) Question Set: 3 (a) What is Slack Time? What are the basic differences between Regression and Correlation? (0.5+1 = 1.5 mark) (b) What is Histogram? Draw a Histogram for these numbers: 2, 3, 5, 2, 1, 1, 8, 9, 3, 6, 8, 7, 4, 3, 9, 4, and 7. (0.5+1 = 1.5 marks) (c) By following all the steps for creating Decision Table, draw and normalise the Decision Table for the following scenario“Agora Supermarket has a policy for cashing customer’s cheque. If the cheque is a Personal cheque for $75.00 or less the cheque can be cashed. If the cheque is a Pay cheque, it can be cashed for over $75.00 provided that the financial organisation, that issues the check, is an organisation Accredited by the Agora Supermarket.” (3+2 = 5 marks) (d) The control chart shown below was produced by a manufacturing production line. The probability distribution shown on the left of the chart is the distribution that the process follows when it is showing Common Cause Variation (an enlarged plot of the distribution is shown below for clarity). The y-axis measures the standard deviations of the process. Answer the following questions based on this chart. 1. What does Common Cause Variation mean? (1 mark) 2. What is the name of the distribution shown in the plot? (0.5 marks) 3. If the y-axis of the plot shows the standard deviations of the process, where would the UCL (upper control limit) and LCL (lower control limit) usually be set? (0.5 marks) (e) The control chart shown below is the same as the previous chart but now it is not in statistical control, it is showing Special Cause Variation. The UCL and LCL are the same as the answer to the previous question. Answer the following questions based on this chart 1. There are three different types of Special Cause Variation shown in the plot, each is circled and labelled i, ii and iii. Name these three types of Special Cause Variation. (1 mark) 2. If the process were in statistical control, what percentage of all data points should fall within ±1 standard deviation of the centre line? (0.5 marks) 3. If the UCL and LCL are set at ±3 standard deviations, how many false alarms per thousand data points should be expected? (0.5 marks) (f) A client comes to you and specifies that they would like you to produce bolts with a target diameter of 2cm and an Upper Specification Limit (USL) of 2.05cm and a Lower Specification Limit (LSL) of 1.95cm.