My x = 7

2 You, a product development manager in a global pharmaceutical company, are undertaking a project to develop a new vaccine for COVID-19. Due to the urgent request from the Ministry of Health, your CEO wants to know when the project can be completed. You have identified six sub- tasks and also obtained the time duration of those tasks, shown in the table below. Task Optimistic time Most likely time (month) Pessimistic time (month) Immediate Predecessor (month) A 2 7 8 None B 6 7 12 A C X X + 3 X + 5 A D 8 9 11 A E 3 5 6 B, C, D F 1 4 5 E As you see in the table above, your time duration information is incomplete. Therefore, you have collected additional data and figured that, for the unknown optimistic time (X) of task C, you can actually use the third number that appears in your student ID number (e.g., X = 5 if your student ID number is '245397987' or X = 8 if your student ID number is '798312486') To have full marks, you need to show your workings. For any decimals in your workings including final answers, round off to one decimal place if applicable. To organize your answers well, you may add bullet points and/or tables in your answers. You can copy and paste the sub-questions (1-8) in your text box and then start typing your answers. 1. What is your student ID? 2. What is your 'X'? 3. Identify all paths: 4. What are the expected duration (path length) and path variance of all identified paths? 5. What are the critical path, its expected duration (length), and its path variance? 6. What is the probability of completing the project (along the critical path) within three months earlier than your expected duration? 7. By how many months are you 90% sure of completing the project (along the critical path)? 8. Suppose your company receives a certain amount of funding from the government to reduce the time (i.e., crashing) to complete the project. Briefly explain how you could establish the best crashing plan