1. **Problem Statement:** We need to find the maximum height of a truck that can travel from Start to Finish along the roads shown, where each road has a height limit. 2. **Understanding the Problem:** The truck must travel from Start to Finish through a path where the minimum height limit on that path is as large as possible. This is a classic problem of finding the path with the maximum bottleneck capacity. 3. **Key Idea:** The maximum truck height is limited by the smallest height limit on the chosen path. So, we want to find a path from Start to Finish where the minimum height limit on the edges is maximized. 4. **Given Heights on Roads:** - Start to next node: 180 - Next node to another node: 200 - Left side going upwards: 70 - Top-left to top-middle: 50 - Top-middle to top-right: 100 - Top-right to near Finish: 95 - Near Finish to Finish: 75 - Middle lower path: 80 - Top-middle to middle-right: 90 5. **Possible Paths and Their Minimum Heights:** - Path 1: Start (180) -> next node (200) -> left side up (70) -> top-left to top-middle (50) -> top-middle to top-right (100) -> top-right to near Finish (95) -> near Finish to Finish (75) - Minimum height = min(180, 200, 70, 50, 100, 95, 75) = 50 - Path 2: Start (180) -> next node (200) -> middle lower path (80) -> near Finish to Finish (75) - Minimum height = min(180, 200, 80, 75) = 75 - Path 3: Start (180) -> next node (200) -> top-middle to middle-right (90) -> near Finish to Finish (75) - Minimum height = min(180, 200, 90, 75) = 75 6. **Comparing Minimum Heights:** - Path 1 minimum height: 50 - Path 2 minimum height: 75 - Path 3 minimum height: 75 7. **Conclusion:** The maximum height of a truck that can travel from Start to Finish is the maximum of these minimum heights, which is $\boxed{75}$. This means the truck height cannot exceed 75 to safely travel from Start to Finish along the roads.