6. [30 points] An app design project consists of following activities. Times are given in weeks. Activity Description Immediate Optimistic Most Likely Pessimistic Predecessor Time Time Time A Prob. Def. 1 2 3 B Sys. Analysis A 4 5 6 C Design 1/0 B 4 4.5 8 D Design DB B 13 14 21 E Develop Input C 6 8 10 F Develop Output C 8 9 16 G Develop DB D 1.5 1.75 3.5 H Test System E, F, G 4.5 5.5 9.5 - Implement H 3 5 7 . 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 30 weeks? Show all work. c. Which activities would you focus on in order to get the project back on schedule? Why? Explain in 2-3 sentences. d. Assume that "Systems Analysis" (B) actually finished at 8 weeks, "Design I/0" (C) actually finished at 15 weeks, and "Design Database" (G) actually finished at 19 weeks. (Note that this is not the duration of activity). Recalculate the expected project completion time. Show all work. e. Using MS Project (or any other software), create a Gantt chart for the project