Consider the PERT project with the following data table (time in weeks) and the network diagram below Activity | Preceding Optimistic Most likely Pessimistic Expected Variance activity completion completion completion activity time time time completion time A None 5 6 7. None 4 5 18 A 4 15 20 D B, C 3 4. 5 0.11 4 17 I E A 16 18 0.11 Activity-On-Node (AON) Network diagram: E End Start D E End Start B D (a) Complete missing values from the above table. (b) Complete the table below: Determine the Earliest Start Time (ES), Earliest Finish Time (EF), Latest Start Time (LS), Latest Finish Time (LF), and the Slack time for each of the activities. Activity ES EF LS Slack A B. C D E (c) Determine: The Critical Path Length (i.e., project duration), the Critical Activities, and the Project Standard Deviation. (d) Calculate the probability of completing the project in 19 days. (e) Assuming that there is an 80% chance of completing project on time, what is the expected duration of such a project? The "Nintendo top management has decided to conduct a research study regarding the potential of a new product realization. The conclusion of such a study should include recommendations with regard to procedures implementation in the production and marketing department. The list of activities required for the new product research study, their time duration (in weeks), and the project network are presented below. Activity Activity Description Normal Time Immediate Predecessors A 6 B 2 C A 3 D A E A 3 To develop technical specification project To develop marketing plan To create logistics maps To build a prototype To make brochures for the advertising company To estimate new product related expenses Preliminary device testing To conduct market research Prepare price report To prepare a final summary report F C 2 G D 3 B.E 4 H H 2 E.GI 2 C F A D G Start E B H (e) The duration of some activities can be reduced by one week ONLY at the following cost per week: A ($4,000): C ($1,000); D ($3,000); E ($1,200); F ($500); G ($900), H (S2,000) and I ($700). Determine the activities to be shortened such that the new product research study project duration becomes 14 weeks. Show your work