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Please sove this so that exactly I write this solution in my exam 

To solve this problem, we'll follow the steps mentioned in the question. Let's go through each part in detail:

### Table Information:
The table provides details for six activities in a project. Each activity has:
- Normal time (NT) and Crash time (CT) in days.
- Normal cost (NC) and Crash cost (CC) in rupees.

### Steps to Solve:

#### (i) Draw the network diagram of the project.

To create the network diagram:
1. **Identify Activities and Predecessors**: Usually, there would be details on which activity precedes which, but it's not provided here. If we assume these activities are sequential, then activity A precedes B, which precedes C, and so on.
2. **Draw Nodes**: Draw nodes representing the start and end of each activity.
3. **Draw Arrows**: Connect the nodes with arrows to represent the activities. Label each arrow with the activity name and its duration.

#### (ii) Calculation of Cost per Unit Time (Crash cost per day):
\[ \text{Cost per unit time} = \frac{\text{Crash Cost} - Normal Cost}{\text{Normal Time} - Crash Time} \]

Let's calculate this for each activity:

1. **Activity A:**
   \[
   \text{Cost per unit time} = \frac{600 - 400}{9 - 7} = \frac{200}{2} = 100 \text{ Rs/day}
   \]
2. **Activity B:**
   \[
   \text{Cost per unit time} = \frac{400 - 300}{8 - 6} = \frac{100}{2} = 50 \text{ Rs/day}
   \]
3. **Activity C:**
   \[
   \text{Cost per unit time} = \frac{1100 - 1000}{10 - 8} = \frac{100}{2} = 50 \text{ Rs/day}
   \]
4. **Activity D:**
   \[
   \text{Cost per unit time} = \frac{500 - 400}{9 - 7} = \frac{100}{2} = 50 \text{ Rs/day}
   \]
5. **Activity E:**
   \[
   \text{Cost per unit time} = \frac{700 - 450}{7 - 4} = \frac{250}{3} \approx 83.33 \text{ Rs/day}
   \]
6. **Activity F:**
   \[
   \text{Cost per unit time} = \frac{1200 - 1000}{12 - 9} = \frac{200}{3} \approx 66.67 \text{ Rs/day}
   \]

#### (iii) The Critical Path:
- The critical path is the longest path through the network, which determines the minimum time required to complete the project.
- To identify the critical path, we would typically analyze the network diagram and identify the path with the longest duration. Without the exact dependencies between activities, we assume a simple sequential path.
- Add the normal times: \( 9 + 8 + 10 + 9 + 7 + 12 = 55 \) days.
  
Since no specific details are provided about the dependencies, this could be one of the longest possible paths.

#### (iv) Minimum Total Cost of Project:
- The minimum total cost involves crashing activities in such a way that we reduce the total project time without increasing the cost disproportionately.
- First, compute the total cost without crashing:
  \[
  \text{Total Normal Cost} = 400 + 300 + 1000 + 400 + 450 + 1000 = 3550 \text{ Rs}
  \]

- For crashing, prioritize activities with the least cost per unit time (calculated above). However, crashing might need to be done until the critical path’s duration is reduced to the target project time.
  
  Summing the costs based on crashing might vary. If full crashing is considered:

  **Assuming each activity is crashed to the minimum time:**
  - Crash cost total: \( 600 + 400 + 1100 + 500 + 700 + 1200 = 4500 \text{ Rs} \)

This is a rough outline of how to proceed. The exact details of the critical path and the crashing sequence require more specific data about dependencies.

Would you like to discuss this further or need a more detailed explanation?

Learn how to optimize project activities' costs using the Critical Path Method. This problem involves calculating crash costs and determining the critical path for efficient project completion. Suitable for advanced college students and professionals.

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