9.The common region between all the constraints of the LPP is called
(1 Point)

basic solution space

feasible solution space

optimal solution space

solution space

In the context of Linear Programming Problems (LPP), the common region that satisfies all the constraints is referred to as the **feasible solution space**. This is the set of all points that meet all the constraints of the problem.

Here are the terms explained:

1. **Basic Solution Space**: This typically refers to the set of solutions obtained by setting \( n - m \) variables to zero in a system of \( m \) linear equations with \( n \) variables.
   
2. **Feasible Solution Space**: This is the set of all possible solutions that satisfy all of the constraints of the linear programming problem.

3. **Optimal Solution Space**: This refers to the set of solutions within the feasible solution space that optimize (maximize or minimize) the objective function.

4. **Solution Space**: This is a broader term that can refer to all potential solutions of the problem, not necessarily satisfying all constraints.

Thus, the correct answer is:

**feasible solution space**

Would you like more details or have any questions?

Here are five related questions to expand on this topic:

1. What is the difference between a feasible solution and an optimal solution in LPP?
2. How do you determine if a solution is feasible in a linear programming problem?
3. What is the significance of the feasible solution space in solving an LPP?
4. Can a feasible solution be non-optimal? Provide an example.
5. What methods can be used to find the feasible solution space in linear programming?

**Tip:** Always ensure that all constraints are carefully considered when defining the feasible solution space in linear programming problems.

9. The common region between all the constraints of the LPP is called

Explore the concept of the feasible solution space in Linear Programming Problems (LPP), where all constraints are satisfied. Learn how this relates to optimization problems and key mathematical principles. Ideal for students in Grades 11-12 studying linear programming.

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