This is a project management problem involving activities for an urban renewal project. It involves:

1. Drawing the network diagram for the given activities.
2. Identifying the critical path and calculating the total float and free float for each activity.

Information Provided:

• Activities and their descriptions:
  • A: Prepare preliminary sketches, 2 days, no predecessor.
  • B: Outline specifications, 1 day, no predecessor.
  • C: Prepare drawings, 3 days, predecessor A.
  • D: Write specifications, 2 days, predecessors A and B.
  • E: Run off prints, 1 day, predecessors C and D.
  • F: Have specification, 3 days, predecessors B and D.
  • G: Assemble bid packages, 1 day, predecessors E and F.

Let's proceed step-by-step:

Part (a) - Network Diagram

The first step is drawing the network diagram using the given activities and predecessors. Here's a brief outline of how the network looks:

• A and B are starting activities.
• C depends on A.
• D depends on A and B.
• E depends on C and D.
• F depends on B and D.
• G depends on E and F.

Part (b) - Critical Path and Float Calculation

• Critical Path is the longest path through the network, which determines the project duration.
• Float is the amount of time that an activity can be delayed without delaying the project.

I'll calculate the critical path, total float, and free float using this information. Give me a moment to do the calculations.### Results:

1. Project Duration: 8 days.

2. Critical Path: Activities A → D → F → G form the critical path. This is the sequence of activities that determine the minimum project duration.

3. Total Float (Total delay an activity can have without affecting the project completion):

   • A: 0 days (on the critical path)
   • B: 1 day
   • C: 1 day
   • D: 0 days (on the critical path)
   • E: 1 day
   • F: 0 days (on the critical path)
   • G: 0 days (on the critical path)

4. Free Float (The amount of time an activity can be delayed without delaying the next activity):

   • A: 0 days
   • B: 1 day
   • C: 0 days
   • D: 0 days
   • E: 1 day
   • F: 0 days
   • G: 0 days

Would you like more details on any specific part of the calculation or diagram?

Next Steps:

1. Can you identify what happens if activity B takes 2 days instead of 1?
2. How would adding a new activity change the network?
3. Can any activities be shortened to reduce the project duration?
4. What would happen if one activity on the critical path is delayed?
5. How could we use this information to optimize resource allocation?

Tip: Always monitor critical path activities closely since any delay will directly affect the overall project timeline.