Let's solve the problem step by step based on the image provided. Here’s how we’ll approach it:

### **Step 1: Network Diagram Construction**
To draw the network diagram, we'll need to identify each activity's dependencies. However, this information isn't explicitly provided in the table. Typically, this would involve connecting activities in the order they need to be completed, based on given dependencies (e.g., Activity B can only start after Activity A is completed).

### **Step 2: Identifying the Critical Path**
The critical path is the sequence of activities that determine the minimum project duration. It’s the longest path through the network diagram. To find the critical path, we must:
1. List all possible paths through the network.
2. Calculate the duration for each path.
3. The path with the longest duration is the critical path.

### **Step 3: Crashing Costs**
Crashing a project involves reducing the time of activities along the critical path, which usually increases costs. The goal is to determine the minimum time for the project at the lowest additional cost.

### **Details from the Table**
From the table, we have the following activities (simplified view):

| Activity | Time (Normal) | Cost (Normal) | Time (Crash) | Cost (Crash) |
|----------|---------------|---------------|--------------|--------------|
| A        | 10 days       | ₹1000         | 8 days       | ₹1400        |
| B        | 7 days        | ₹800          | 5 days       | ₹1100        |
| C        | 9 days        | ₹900          | 7 days       | ₹1200        |
| D        | 5 days        | ₹500          | 3 days       | ₹800         |
| E        | 11 days       | ₹1100         | 9 days       | ₹1500        |
| F        | 8 days        | ₹600          | 6 days       | ₹900         |
| G        | 6 days        | ₹700          | 4 days       | ₹1000        |

### **Calculations**

#### 1. **Normal Duration and Cost**
Sum the normal duration and normal cost of all activities:

- **Normal Time:** 10 + 7 + 9 + 5 + 11 + 8 + 6 = **56 days**
- **Normal Cost:** ₹1000 + ₹800 + ₹900 + ₹500 + ₹1100 + ₹600 + ₹700 = **₹5600**

#### 2. **Critical Path Calculation**
The critical path would require the sequence and dependency of activities. Assuming a simple linear dependency (A → B → C → ...), the critical path is the one with the maximum time and cost associated.

- **Critical Path Time:** Maximum time path = 56 days (sum of all individual normal times)
- **Critical Path Cost:** Normal = ₹5600

#### 3. **Project Crashing**
Calculate the cost for crashing:

- **Crashing Costs:** (Crash cost - Normal cost) per activity:
  - A: (₹1400 - ₹1000) = ₹400 for 2 days reduction
  - B: (₹1100 - ₹800) = ₹300 for 2 days reduction
  - C: (₹1200 - ₹900) = ₹300 for 2 days reduction
  - D: (₹800 - ₹500) = ₹300 for 2 days reduction
  - E: (₹1500 - ₹1100) = ₹400 for 2 days reduction
  - F: (₹900 - ₹600) = ₹300 for 2 days reduction
  - G: (₹1000 - ₹700) = ₹300 for 2 days reduction

Total cost to crash all activities:
- Total additional cost = ₹400 + ₹300 + ₹300 + ₹300 + ₹400 + ₹300 + ₹300 = **₹2300**

- **Crashing Time:** Assuming all are fully crashed, new time = 56 days - (2 days x 7 activities) = **42 days**

- **Total Crashing Cost:** ₹5600 (Normal) + ₹2300 (Additional) = **₹7900**

### **Final Results**
- **Critical Path Duration (Normal):** 56 days
- **Critical Path Cost (Normal):** ₹5600
- **Total Crashed Duration:** 42 days
- **Total Crashed Cost:** ₹7900

If any specific path is given or the dependency details are needed, the exact critical path may vary.

Would you like more details on how I determined this, or do you have any questions on how to approach a similar problem?

Here are 5 related questions:
1. Do you want to see how to derive the critical path using different paths and durations?
2. Would you like to learn more about the significance of the critical path in project management?
3. Are you interested in how to optimize project costs and time using advanced crashing techniques?
4. Would you need help in drawing a detailed network diagram with hypothetical dependencies?
5. Do you want to explore other methods like PERT (Program Evaluation and Review Technique) for project management?

**Tip**: Always ensure you have a clear understanding of the dependencies between activities before determining the critical path to avoid errors in the network diagram.

Explore how to solve project management problems using the critical path method and crashing costs analysis. Learn about determining the critical path, crashing activities to reduce project duration, and calculating additional costs involved. Suitable for professionals in project management and engineering fields.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation