3. (25%) A hardware development project has eight activities and six events. The activities and their expected completion times are as follows: Activity AB AC ADC DB FCEEF D-F Days 2-5-8 2-4-6 4-7-10 2-5-8 6-9-12 4-4-4 3-6-9 4 - 7-10 (a) Represent the program in the form of the PERT network. (b) Determine the critical path of the network. (c) Calculate the probability that the project will take more than 16 days to complete. (d) If an activity is added between event B and event D ( B D; 2-5-8), modify the PERT network and show how the critical path would be changed. In this case, what is the probability that the project will take less than 17 days to complete? (e) If the expected completion times of the following activities can be shortened as below, how will that affect the critical path in (b) and (d)? A+D (3-6-9), B+F (7-7-7), C E (1-3-5)