Question 1) Activity Predecessor Optimistic Pessimistic A B D Most Likely 7 21 33 16 19 9 9 5 14 21 14 18 7 7 A 15 22 45 30 26 11 17 E B F G H I B B, C D DE F G HI 8 3 8 4 8 5 4 5 J K 6 21 a) (10 points) Develop an AOA diagram for the given activities. b) (5 points) Find the critical path and project completion time. c) (10 points) Find the probability of completing the project at 58 days. d) (10 points) The project manager is promised $12,000 if the project completed in less than 50 days, $8,000 if the project completed within 50-53 days, and no reward if the project goes above 53 days. What is the expected value of the manager's bonus? Question 2) (25 points) An activity on the critical path of a project was scheduled to be completed within 12 weeks, with a budget of $8,000. During a performance review, which took place 7 weeks after the activity was initiated, it was found that 50% of the work had already been completed and the actual cost was $4,500. Discuss the situation as a project manager by making the necessary calculations. Question 3) (20 points) Write down the scope of your intradisciplinary project and choose one risk and identify, analyze, and develop plan for this risk Question 4) (20 points) In the middle of the execution, a change is detected. How should this process be managed