VIPSolutions4. Four engineers are to work on 4 projects of MMQ engineering services company. The project managers need to decide which engineer should be assigned on each project. Each engineer charges different fees on each project, due to the distance of the projects and complexity. The cost is given below. [~~ [PROECT1 [PROJECT2 [PROJECT3 [PROJECT | [ners [12 [15 [1 [5]
Question:
4. Four engineers are to work on 4 projects of MMQ engineering services company. The project
managers need to decide which engineer should be assigned on each project. Each engineer charges
different fees on each project, due to the distance of the projects and complexity. The cost is given
below.
[~~ [PROECT1 [PROJECT2 [PROJECT3 [PROJECT |
[ners [12 [15 [1 [5]
This is AI generated Response.
Asked by: Test User 100107
Created at: 2025-05-07 18:28:15
Asked by: Test User 100107
Created at: 2025-05-07 18:28:15
Final Answer:
Rendered
Raw Text
Did you like this answer?
This is a classic **assignment problem**, where we want to assign 4 engineers to 4 projects such that each engineer gets exactly one project, and the total cost is minimized.
Here's the cost table:
| | Project 1 | Project 2 | Project 3 | Project 4 |
|---------|-----------|-----------|-----------|-----------|
| **Engr 1** | 17 | 16 | 13 | 22 |
| **Engr 2** | 15 | 14 | 13 | 19 |
| **Engr 3** | 19 | 20 | 23 | 19 |
| **Engr 4** | 12 | 15 | 11 | 15 |
Let's solve this using the **Hungarian Method** (or you can brute-force since it's just 4x4):
### Try All Possibilities (Brute Force)
Let's calculate the total cost for all possible assignments.
However, to save time, let's look for the minimum cost in each column and try assigning accordingly:
#### Step 1: Assign minimum cost in each project (column):
- Project 1: **Engr 4** (12)
- Project 2: **Engr 2** (14)
- Project 3: **Engr 4** (11) (already assigned to Project 1)
- Project 4: **Engr 2** (19) (already assigned to Project 2)
But we can't assign one engineer to more than one project. Let's try possible combinations:
#### Step 2: List all possible assignments and sum their costs:
1. **Engr 1 - Project 1 (17), Engr 2 - Project 2 (14), Engr 3 - Project 3 (23), Engr 4 - Project 4 (15)**
Total = 17 + 14 + 23 + 15 = **69**
2. **Engr 1 - Project 1 (17), Engr 2 - Project 3 (13), Engr 3 - Project 4 (19), Engr 4 - Project 2 (15)**
Total = 17 + 13 + 19 + 15 = **64**
3. **Engr 1 - Project 3 (13), Engr 2 - Project 1 (15), Engr 3 - Project 4 (19), Engr 4 - Project 2 (15)**
Total = 13 + 15 + 19 + 15 = **62**
4. **Engr 1 - Project 3 (13), Engr 2 - Project 2 (14), Engr 3 - Project 4 (19), Engr 4 - Project 1 (12)**
Total = 13 + 14 + 19 + 12 = **58**
5. **Engr 1 - Project 3 (13), Engr 2 - Project 2 (14), Engr 3 - Project 1 (19), Engr 4 - Project 4 (15)**
Total = 13 + 14 + 19 + 15 = **61**
6. **Engr 1 - Project 2 (16), Engr 2 - Project 3 (13), Engr 3 - Project 4 (19), Engr 4 - Project 1 (12)**
Total = 16 + 13 + 19 + 12 = **60**
7. **Engr 1 - Project 2 (16), Engr 2 - Project 4 (19), Engr 3 - Project 3 (23), Engr 4 - Project 1 (12)**
Total = 16 + 19 + 23 + 12 = **70**
8. **Engr 1 - Project 4 (22), Engr 2 - Project 2 (14), Engr 3 - Project 3 (23), Engr 4 - Project 1 (12)**
Total = 22 + 14 + 23 + 12 = **71**
#### The minimum total cost is **58**.
### **Best Assignment:**
- **Engr 1 → Project 3 (13)**
- **Engr 2 → Project 2 (14)**
- **Engr 3 → Project 4 (19)**
- **Engr 4 → Project 1 (12)**
**Minimum Total Cost: 58**
---
If you need the step-by-step Hungarian method, let me know!
📢 Instructions:
- Ask anything relatd to above question only.
- For new Question goto :