Date:.11.4.2021 Date:11.4. 2021 Page 2 Question One Question One A new project is to be completed. The following activities need to be completed in the order shown, where times are in weeks. Activity Immediate predecessor Optimistic Time (a) Most Likely Time (m) Pessimistic time (b) Variance A - 4 5 12 1.7778 B - 1 1.5 5 0.4444 C A 2 3 4 0.1111 D A 3 4 11 1.7778 E A 2 3 4 0.1111 F C 1.5 2 2.5 0.0278 G D,E 1.5 3 4.5 0.2500 H B,F 2.5 3.5 7.5 0.6944 I H 1.5 2 2.5 0.0278 J F,G,I 1 2 3 0.1111 You must use two decimal places at all times for expected times when they are not integer (you are not permitted to round off to integers). (a) Draw the activity network for this problem (6 marks) (b) Determine the Expected Times. (1 mark) (c) Determine the activity schedule (ES, EF, LS, and LF) as well as slack. (7 marks) (d) Determine and state the critical path for this project. (1 mark) (e) What are the expected time and the variance of the project? (2 marks) (f) What is the probability that the project is completed in 18 or fewer weeks(1 mark) (g) What date should be set such that there is a 94% chance of completion within that time? (2 marks) DO NOT WRITE OR TYPE ON THE BACK OF THIS SHEET: USE ONE SIDE ONLY INSTRUCTIONS: Each page must be signed by the FIRST AND SECOND EXAMINERS. Completed forms should be handed to the Senior Assistant Registrar (Assessment, Awards & Records). Please indicate below the version of the question paper: Main Paper Alternate 1 Alternate 2 ..................................... ............................................ First Examiner Second Examiner Date:.11.4.2021 Date:11.4. 2021 Page 3 Question 2 CWD Investments Ltd must decide between three alternative investments stocks and bonds and the money market. The return for each investment, given three future economic conditions, is shown in the following payoff table: Investment Improve Steady Decline Stocks $10,000 $6,000 ($1,000) Bonds 9,000 6,500 2,000 Money market 7,000 4,500 3,000 (a) Which alternative should CWD choose under the maximax criterion? (1 mark) (b) Which option should CWD choose under the maximin criterion? (1 mark) (c) Which option should CWD choose under the LaPlace criterion? (2 marks) (d) Which option should CWD choose with the Hurwicz criterion with = 0.2? (2 marks) (e) Using a minimax regret approach, what alternative should CWD choose? (4 marks) (f) After reading about economic predictions, CWD has assigned the probability that the economy will improve , or be steady or decline at 20%, 50% and 30 %. Using expected monetary values, what option should be chosen and what is that optimal expected value? (4 marks) (g) What is the most that CWD should be willing to pay for additional information? Use Expected Regret (3 marks) (h) Use the alternative method to verify EVPI (3 marks)