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You have provided two problems: an assignment problem and a travelling salesman problem. I will go through both problems and solve one of them based on your preference.

### Problem (6) - **Assignment Problem**
This is an assignment problem where we need to assign workers (A, B, C, D, E) to tasks (V, W, X, Y, Z) in such a way that the total cost is minimized. The cost matrix is:

|     | V  | W  | X  | Y  | Z  |
|-----|----|----|----|----|----|
| **A** |  3 |  5 | 10 | 15 |  8 |
| **B** |  4 |  7 | 15 | 18 |  8 |
| **C** |  8 | 12 | 20 | 20 | 12 |
| **D** |  5 |  5 |  8 | 10 |  6 |
| **E** | 10 | 10 | 15 | 25 | 10 |

The assignment problem can be solved using **Hungarian Method**.

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### Problem (7) - **Travelling Salesman Problem (TSP)**
This is a classical travelling salesman problem where we need to find the shortest possible route that visits each city (A, B, C, D, E) exactly once and returns to the starting point. The cost matrix is:

|     | A  | B  | C  | D  | E  |
|-----|----|----|----|----|----|
| **A** |  ∞ | 14 | 10 | 24 | 41 |
| **B** |  6 |  ∞ | 10 | 12 | 10 |
| **C** |  7 | 13 |  ∞ |  8 | 15 |
| **D** | 11 | 14 | 30 |  ∞ | 17 |
| **E** |  6 |  8 | 12 | 16 |  ∞ |

The problem can be solved using **Branch and Bound method** or **Dynamic Programming**.

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Please let me know which problem you would like to proceed with, and I will provide a detailed solution.

Solve the assignment problem or the travelling salesman problem.

This solution walks through how to solve an assignment problem using the Hungarian Method and a travelling salesman problem using optimization techniques such as Branch and Bound or Dynamic Programming. The detailed steps help minimize costs and find optimal routes.

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