Certainly, let's address each of the tasks listed one by one:

a. the network diagram

Given the nature of this platform, I'm unable to draw and display images directly. However, I can describe how the network diagram can be drawn using the given project information.

To create the network diagram:

1. Begin by drawing a circle labeled Start.
2. From Start, draw an arrow to another circle labeled, since A has no predecessors.
3. From A, draw an arrow to B, as B has A as its predecessor.
4. Draw an arrow from B to C and D since C and D both have B as their predecessor.
5. Draw an arrow from C to E, and since [Occurrence of "ooeu" is a typo, assuming it to mean "D"], also draw arrow from D to E.
6. Draw two arrows emanating from E; one to F and another to G, as both have E as their predecessor.
7. Finally, from F G, draw two arrows converging onto a final node labeled End.

b. Calculate the total duration of the project

The total duration of the project is the length of the longest path through the network, representing the shortest possible completion time for the entire project. This path is known as the critical path, which we'll identify in part c.

c. Identify the critical path of the project

To identify the critical path, you need to calculate the earliest start time (EST) latest start time (LST) for each activity.

• Start at the beginning, A has a duration of 10 days- B, which follows A, adds 2 days, putting us at 12 days by the completion of.
• Both C and D follow B and so would both start at day 12.
• C adds5 more days, and D adds 10 days. Thus when C completes, we at day 17, but completion of D will be day 22.
• E cannot start until both C and D are complete, so E would begin day 22.
• E takes 20 days, which means we would be at 42 upon its completion.
• F and G follow E, starting at day 42; F adds 5 days and G adds 15 days.
• The path finishing with F will have taken days whereas the path finishing with G will have taken 57 days.

Therefore, the critical path is A - B - - E - G, with a duration of 57 days.

d. What is, give examples (15 marks)

CPA stands for Critical Path Analysis. It's a method used to predict project duration by analyzing which sequence of activities (which path) has the least amount of scheduling flexibility. In other words, which path if delayed, would delay the entire project. The critical path is the longest necessary path through a network of activities.

Examples of CPA:

1. Construction Project: In building a house, the critical path would include foundations being laid before the walls are erected, and walls before the roof is added. the laying of the foundations is delayed, it postpones everything else.

2. Product Launch: For a new product launch, a critical path might include finalizing the product design, then manufacturing, followed by marketing and distribution setup. If there's a delay in finalizing the design, can't commence, affecting all subsequent activities.

3. Software Development: In software development, the critical path might include requirements analysis, followed by design, development, and testing. A delay in completing the requirements analysis leads to a delay in all other phases, hence prolonging project completion.

Critical Path Analysis helps project managers to prioritize activities, allocate resources efficiently, and mitigate potential risks to the project timeline.