The assignment problem is solved by ….

Options

A. Simplex method
B. vector method
C. Hungarian method
D. Graphical method

Answer

To solve the question "The assignment problem is solved by…", we will analyze the options provided and determine the correct method used to solve assignment problems.

### Step-by-Step Solution:

1. **Understanding the Assignment Problem**:
The assignment problem is a special case of the transportation problem in linear programming. It involves assigning a number of resources (like workers) to an equal number of tasks (like jobs) in such a way that the total cost (or time) of the assignment is minimized.

**Hint**: Recall that the assignment problem deals with matching resources to tasks efficiently.

2. **Evaluating the Options**:
- **a. Simplex Method**: This is a widely used algorithm for solving linear programming problems, but it is not specifically designed for assignment problems.
- **b. Vector Method**: This is not a standard method for solving assignment problems.
- **c. Hungarian Method**: This is a combinatorial optimization algorithm that specifically solves assignment problems. It is efficient and provides an optimal solution.
- **d. Graphical Method**: This method is used for solving linear programming problems with two variables, but it is not applicable for assignment problems.

**Hint**: Compare the characteristics of each method with the requirements of the assignment problem.

3. **Identifying the Correct Method**:
Based on the definitions and characteristics of the methods:
- The **Hungarian Method** is specifically designed for solving assignment problems and is the most efficient way to find the optimal assignment.

**Hint**: Remember that the Hungarian Method is named after the mathematicians who developed it and is particularly effective for problems involving assignments.

4. **Conclusion**:
Therefore, the assignment problem is solved by the **Hungarian Method**.

### Final Answer:
The assignment problem is solved by **c. Hungarian Method**.