1. **State the problem:** We have a project with activities, durations, and dependencies. We need to find the minimum project completion time, critical activities, floats, and analyze scheduling constraints. 2. **Construct the activity network:** - Activities: A (Planning, 2 days), B (Write script, 1 day), C (Choose locations, 1 day), D (Casting, 0.5 days), E (Rehearsals, 2 days), F (Get permissions, 1 day), G (First day filming, 1 day), H (First day edits, 1 day), I (Second day filming, 0.5 days), J (Second day edits, 2 days), K (Finishing, 1 day). - Predecessors: - A has none. - B, C, D depend on A. - E depends on B and D. - F depends on C. - G depends on E and F. - H depends on G. - I depends on G. - J depends on H and I. - K depends on J. 3. **Calculate earliest start (ES) and earliest finish (EF):** - A: ES=0, EF=2 - B: ES=2, EF=3 - C: ES=2, EF=3 - D: ES=2, EF=2.5 - E: ES=max(B, D)=3, EF=5 - F: ES=C=3, EF=4 - G: ES=max(E, F)=5, EF=6 - H: ES=G=6, EF=7 - I: ES=G=6, EF=6.5 - J: ES=max(H, I)=7, EF=9 - K: ES=J=9, EF=10 Minimum project completion time is EF of K = 10 days. 4. **Calculate latest finish (LF) and latest start (LS) backward from project end (10 days):** - K: LF=10, LS=9 - J: LF=LS of K=9, LS=7 - H: LF=LS of J=7, LS=6 - I: LF=LS of J=7, LS=6.5 - G: LF=min(LS of H, LS of I)=6, LS=5 - E: LF=LS of G=5, LS=3 - F: LF=LS of G=5, LS=4 - B: LF=LS of E=3, LS=2 - D: LF=LS of E=3, LS=2.5 - C: LF=LS of F=4, LS=3 - A: LF=min(LS of B, LS of C, LS of D)=2, LS=0 5. **Calculate float for each activity:** Float = LS - ES or LF - EF - A: 0 - B: 2 - 2 = 0 - C: 3 - 2 = 1 - D: 2.5 - 2 = 0.5 - E: 3 - 3 = 0 - F: 4 - 3 = 1 - G: 5 - 5 = 0 - H: 6 - 6 = 0 - I: 6.5 - 6 = 0.5 - J: 7 - 7 = 0 - K: 9 - 9 = 0 6. **Critical activities:** Activities with zero float: A, B, E, G, H, J, K. 7. **Answer (ii): Reasons filming may take longer than minimum time:** - Delays in obtaining permissions or locations. - Resource constraints or unexpected problems during filming. 8. **Answer (iii): Why minimum completion time is longer with Sheona and Tim's restriction:** - Because Sheona and Tim cannot work on multiple activities simultaneously, some activities must be delayed, increasing total time. 9. **Answer (iv)(a): Longest break either can take:** - Total project time = 14 days, minimum = 10 days, so max break = 14 - 10 = 4 days. 10. **Answer (iv)(b): Longest break both can take together:** - Since they work together on planning and finishing (2 + 1 = 3 days), and cannot overlap tasks, the longest combined break is less than or equal to 4 days, but exact depends on scheduling; conservatively, 4 days. 11. **Answer (iv)(c): Float on each activity:** - Same as step 5, but adjusted for 14-day deadline, floats increase by 4 days: - A: 4 - B: 4 - C: 5 - D: 4.5 - E: 4 - F: 5 - G: 4 - H: 4 - I: 4.5 - J: 4 - K: 4 Final answers: - Minimum project completion time: 10 days - Critical activities: A, B, E, G, H, J, K - Float on non-critical activities: C=1, D=0.5, F=1, I=0.5 - Reasons for delay: delays in permissions/locations, resource constraints - Restriction effect: single-tasking increases total time - Longest break either: 4 days - Longest break both: 4 days - Float with 14-day deadline: increased by 4 days for all activities