(SHOW YOUR COMPLETE WORK) The activities needed for a new project your company is undertaking are listed in the following table. The activity times were determined for the project, and were as below. a. Construct the project network diagram using Activity-on-Node (AON) approach. [6 points] b. Determine the earliest start (ES) time, earliest finish (EF) time, latest finish (LF) time, and latest start (LS) time for all project activities on the AON project network diagram. [13 points] c. Determine slack times for all project activities on the AON project network diagram. [6 points] d. Identify the critical path(s) in the project network. [2 points] e. How long will it take to complete the entire project? [2 point] 2. (SHOW YOUR COMPLETE WORK) A project network is shown below, with three time estimates (Optimistic Time-Most Likely Time-Pessimistic Time (in weeks)) for each activity in the network. a. Compute the expected time for each activity in the project network. [8 points] b. Identify and list all possible paths in the project network. Compute the expected duration for each path in the project network. [13 points] c. Identify the critical path(s) in the project network. What is the expected project completion time? d. Compute the variance of each activity on the critical path(s). [3 points] e. Determine the project variance and project standard deviation. [3 points] [4 points] Use the PERT analysis results in 2(c) and 2(e) above to answer questions (f), (g), (h), and (i) below: f. What is the probability that the project can be completed within 36 weeks of its start? [3 points] g. What is the probability that the project can be completed within 27 weeks of its start? [4 points] h. Determine the project deadline that gives this project a 73% chance of on-time completion. [5 points] i. Determine the project deadline that gives this project a 13% chance of on-time completion. [6 points]