1. **State the problem:** We have a project with activities A to G, each with normal and crashed times and costs. We need to find the overall project duration, crash costs per week, and the cost of crashing the project to shorter durations. 2. **Calculate crash cost per week for each activity:** Crash cost per week = \frac{\text{Crashed Cost} - \text{Normal Cost}}{\text{Normal Time} - \text{Crashed Time}} - A: \frac{3100 - 1100}{3 - 2} = \frac{2000}{1} = 2000 - B: \frac{2500 - 2200}{2 - 1} = \frac{300}{1} = 300 - C: \frac{2800 - 1300}{3 - 1} = \frac{1500}{2} = 750 - D: \frac{2500 - 2000}{7 - 3} = \frac{500}{4} = 125 - E: \frac{2100 - 1800}{6 - 3} = \frac{300}{3} = 100 - F: \frac{5460 - 4200}{3 - 1} = \frac{1260}{2} = 630 - G: \frac{2000 - 1600}{4 - 2} = \frac{400}{2} = 200 3. **Find the overall project duration (normal):** Identify the critical path by summing durations along paths: - Path 1: A (3) + D (7) + G (4) = 14 weeks - Path 2: B (2) + E (6) + G (4) = 12 weeks - Path 3: C (3) + F (3) = 6 weeks The longest path is Path 1 with 14 weeks, so overall duration is 14 weeks. 4. **Lowest crash cost per week:** From step 2, lowest is E with 100 per week. 5. **Highest crash cost per week:** From step 2, highest is A with 2000 per week. 6. **Which activity to crash first to shorten overall duration?** Crash activities on the critical path (A, D, G). Among these, D has the lowest crash cost per week (125), so crash D first. 7. **Crash project from 14 to 11 weeks (reduce 3 weeks):** Critical path activities and max crash weeks: - A: 1 week - D: 4 weeks - G: 2 weeks Crash D fully (4 weeks) reduces duration by 4 weeks, but we only need 3 weeks reduction. So crash D by 3 weeks. Cost = 3 weeks * 125 = 375 8. **Crash project from 14 to 9 weeks (reduce 5 weeks):** Crash D fully (4 weeks) = 4 * 125 = 500 Need 1 more week reduction: Next cheapest on critical path is G (200 per week), crash G by 1 week = 200 Total cost = 500 + 200 = 700 **Final answers:** - Overall duration: 14 weeks - Lowest crash cost per week: E - Highest crash cost per week: A - Activity to crash first: D - Cost to crash to 11 weeks: 375 - Cost to crash to 9 weeks: 700