5. [30 points] Consider a project with following precedence relationships and activity times. Activity Immediate Predecessor Optimistic Time Most Likely Pessimistic Time Time A 2 2.5 6 B 10 11 12 A 5 6.5 11 D B, C 11 13 15 E B 8 9.5 14 F D 4.5 5.5 9.5 G E 3.5 5 6.5 H F, G 6.5 7.5 11.5 a. Calculate the expected activity duration (t), variance for each activity, ES, EF, LS, and LF times and the slack for each activity. Show the values in a table (activity schedule). What is the critical path for the project? Show all work to earn credit. b. What is the probability of completing the project in 35 weeks? Show all work to earn credit. c. If the activity B can be finished in 10 weeks, D in 11 weeks, and E in 8 weeks, recalculate the expected project completion time. Show all work. d. Using MS Project (or any other software), create a Gantt chart for the project based on ES and EF times. If you worked in a paper, you must scan the work and insert it into the .docx or .pdf file with your answers. Separate images of documents are not accepted.