An advertising project manager has developed a program for a new advertising campaign. In addition, the manager has gathered the time information for each activity as shown in the following table. Time Estimates (week) Activity Optimistic Most Likely Pessimistic Immediate Predecessor(s) A 1 4 7 B 2 6 10 3 3 9 B D 6 13 14 A E 4 6 14 A, C F 6 8 16 B G 2 5 8 D, E, F a. Draw a network diagram and identify critical path based on the information above and calculate the expected activity times (round to nearest integer). b. Now, assume that activity E has taken 8 weeks past its anticipated duration to complete. What happens to the project's schedule? Has the duration changed? Is there a new critical path? c. Calculate the activity slacks. What is the total project length? Make sure you fully label all nodes in the network. d. Given the activity variances, what is the likelihood of the project finishing on week 24? e. Suppose you wanted to have a 99% confidence in the project finishing on time. How many additional weeks would your project team need to negotiate for in order to gain this 99% likelihood