1. **Problem Statement:** We have a project with activities A to H, each with durations and dependencies. We need to find the Earliest Start (ES), Earliest Finish (EF), Latest Start (LS), Latest Finish (LF) times, and identify the Critical Path and project completion time. 2. **Step 1: List activities, durations, and predecessors:** - A: duration 4, no predecessor - B: duration 6, predecessor A - C: duration 5, predecessor A - D: duration 3, predecessor B - E: duration 4, predecessor C - F: duration 6, predecessor C - G: duration 5, predecessors D and E - H: duration 2, predecessors F and G 3. **Step 2: Calculate Earliest Start (ES) and Earliest Finish (EF):** - ES for A = 0 (start of project) - EF for A = ES + duration = 0 + 4 = 4 - For B (predecessor A): ES = EF of A = 4 - EF for B = 4 + 6 = 10 - For C (predecessor A): ES = EF of A = 4 - EF for C = 4 + 5 = 9 - For D (predecessor B): ES = EF of B = 10 - EF for D = 10 + 3 = 13 - For E (predecessor C): ES = EF of C = 9 - EF for E = 9 + 4 = 13 - For F (predecessor C): ES = EF of C = 9 - EF for F = 9 + 6 = 15 - For G (predecessors D and E): ES = max(EF of D, EF of E) = max(13, 13) = 13 - EF for G = 13 + 5 = 18 - For H (predecessors F and G): ES = max(EF of F, EF of G) = max(15, 18) = 18 - EF for H = 18 + 2 = 20 4. **Step 3: Calculate Latest Finish (LF) and Latest Start (LS):** - LF for H = EF of H = 20 (project completion time) - LS for H = LF - duration = 20 - 2 = 18 - For G (successor H): LF = LS of H = 18 - LS for G = 18 - 5 = 13 - For F (successor H): LF = LS of H = 18 - LS for F = 18 - 6 = 12 - For D (successor G): LF = LS of G = 13 - LS for D = 13 - 3 = 10 - For E (successor G): LF = LS of G = 13 - LS for E = 13 - 4 = 9 - For B (successor D): LF = LS of D = 10 - LS for B = 10 - 6 = 4 - For C (successors E and F): LF = min(LS of E, LS of F) = min(9, 12) = 9 - LS for C = 9 - 5 = 4 - For A (successors B and C): LF = min(LS of B, LS of C) = min(4, 4) = 4 - LS for A = 4 - 4 = 0 5. **Step 4: Identify the Critical Path:** The critical path is the sequence of activities where ES = LS and EF = LF (no slack). - A: ES=0, LS=0 - B: ES=4, LS=4 - D: ES=10, LS=10 - G: ES=13, LS=13 - H: ES=18, LS=18 Critical Path: A → B → D → G → H 6. **Step 5: Project Completion Time:** The project completion time is the EF of the last activity on the critical path, which is 20 days. **Final answer:** - ES, EF, LS, LF for each activity: | Activity | ES | EF | LS | LF | |----------|----|----|----|----| | A | 0 | 4 | 0 | 4 | | B | 4 | 10 | 4 | 10 | | C | 4 | 9 | 4 | 9 | | D | 10 | 13 | 10 | 13 | | E | 9 | 13 | 9 | 13 | | F | 9 | 15 | 12 | 18 | | G | 13 | 18 | 13 | 18 | | H | 18 | 20 | 18 | 20 | - Critical Path: A → B → D → G → H - Project Completion Time: 20 days