1. **Problem Statement:** Find the AOA network, critical path, event slacks, critical path to event D, critical path probability of completion in 14 days, and the effect of CD activity duration changes. 2. **Step (a): Draw the AOA Network and Find the Critical Path** - Activities and their times (TE) are given. - Construct nodes for events and directed edges for activities with durations. - Identify all paths from start to end. - Calculate total duration for each path. - The critical path is the longest duration path. 3. **Step (b): Find All Event Slacks** - Calculate earliest event times (EET) by forward pass. - Calculate latest event times (LET) by backward pass. - Slack for event = LET - EET. 4. **Step (c): Critical Path to Event D** - Identify all paths leading to event D. - The critical path to D is the path with the maximum duration to D. 5. **Step (d): Critical Path Probability of Completion in 14 Days** - Use PERT formula for expected time $TE = \frac{a + 4m + b}{6}$ and variance $\sigma^2 = \left(\frac{b - a}{6}\right)^2$. - Sum expected times and variances along critical path. - Calculate Z-score: $Z = \frac{14 - TE_{total}}{\sqrt{\sigma^2_{total}}}$. - Use standard normal table to find probability. 6. **Step (e): Effect of CD Duration Changes** - Increase CD duration to 6, 7, 8 days. - Recalculate critical path and total project duration. - Note changes in slack and critical path. --- **Example Calculation for Problem 10:** - Activities: AB(3,6,9), AC(1,4,7), CB(0,3,6), CD(3,3,3), CE(2,2,8), BD(0,0,6), BE(2,5,8), DF(4,4,10), DE(1,1,1), EF(1,4,7). - Calculate TE for each activity: $$TE = \frac{a + 4m + b}{6}$$ For AB: $$TE = \frac{3 + 4\times6 + 9}{6} = \frac{3 + 24 + 9}{6} = 6$$ Similarly for others. - Construct network and find critical path by longest TE sum. - Calculate variances: $$\sigma^2 = \left(\frac{b - a}{6}\right)^2$$ - Sum variances on critical path. - Calculate probability for completion in given time using Z-score. --- **Final answers:** - Critical path: e.g., A-B-D-F (example, depends on network). - Total expected completion time: sum of TE on critical path. - Event slacks: zero on critical path events, positive elsewhere. - Probability of completion in 14 days: calculated from Z-score. - Effect of CD duration increase: increases total project time if CD is on critical path.