The problem outlined involves calculating the minimum time needed to complete a project with 10 activities using estimates from three sources: Carla, Tim, and Martha. Here's a breakdown of what needs to be done:

1. Activity Analysis and Precedence: We are given the project sequence, including predecessor relationships for each task, along with time estimates by Carla (Ta) and Tim (Tb).

2. Part (a): Compare Carla and Tim's Estimates:

   • We need to determine the total project time according to Carla and Tim's estimates and identify the critical tasks for each.

3. Part (b): Calculate using Martha's Formula:

   • Martha's formula to estimate the time for each task is given as: $T_c = \frac{1.5T_a + 1.4T_b + 0.1}{3}$
   • We will apply this formula to each task and then recalculate the total time and critical path.

Steps to Solve:

1. Draw PERT Diagrams: Construct the project network diagram based on the sequence of activities and their precedences.

2. Calculate Critical Path:

   • Use Carla’s and Tim’s estimates to determine the earliest start and finish times, the critical path (i.e., the longest path through the network that determines the total project duration).

3. Calculate Project Duration for Each Estimate:

   • Use Carla’s (Ta), Tim’s (Tb), and Martha’s (Tc) estimates to find the total project duration based on the critical path.

4. Compare Results:

   • Identify whose estimated project completion time is the shortest and which one is the longest.

Would you like me to begin by computing the times for Carla and Tim’s estimates, or would you prefer I focus on creating the PERT diagram first?

Here are five related questions you might explore after this problem:

1. How does the critical path method (CPM) differ from the PERT analysis?
2. How would changes in time estimates (due to risk factors) affect the overall project timeline?
3. What are the benefits of using multiple estimates like Carla’s, Tim’s, and Martha’s in project management?
4. How could resource allocation influence the critical path in a project schedule?
5. Can we apply the same method to real-life projects with hundreds of tasks?

Tip: In project management, identifying the critical path is essential, as it shows which tasks directly impact the project completion time.