What do we call a set of values of the variable satisfying all the constraints ?

Options

A. Optimal solution
B. Feasible solution
C. objective solution
D. None of them

Answer

To solve the question, we need to identify the correct term that describes a set of values of a variable that satisfies all the constraints in a mathematical context, particularly in optimization problems.

### Step-by-step Solution:

1. **Understanding the Question**: The question asks for a specific term that refers to a set of values satisfying all constraints in a mathematical model.

**Hint**: Think about the terminology used in optimization and linear programming.

2. **Analyzing the Options**: We have four options to consider:
- Option 1: Optimal solution
- Option 2: Feasible solution
- Option 3: Objective solution
- Option 4: None of them

**Hint**: Recall the definitions of each term in the context of mathematical optimization.

3. **Defining Each Term**:
- **Optimal Solution**: This refers to the best solution that maximizes or minimizes the objective function, but it may not necessarily satisfy all constraints.
- **Feasible Solution**: This is a set of values that satisfies all the constraints of the problem.
- **Objective Solution**: This term is not commonly used in optimization; it may refer to the solution that achieves the objective but is not a standard term.
- **None of them**: This option suggests that none of the previous terms are correct.

**Hint**: Focus on the definition of a feasible solution, as it directly relates to satisfying constraints.

4. **Identifying the Correct Answer**: Based on the definitions, the term that specifically refers to a set of values satisfying all constraints is the "Feasible Solution."

**Hint**: Confirm that the definition aligns with the question's requirement.

5. **Final Answer**: Therefore, the correct answer is **Option 2: Feasible Solution**.