The area containing all the possible solutions to the problem which are feasible is called ………..

Answer

To solve the question, we need to identify the term that describes the area containing all possible feasible solutions in a linear programming problem. Here’s a step-by-step breakdown of the solution:

### Step-by-Step Solution:

1. **Understanding Linear Programming**:
- Linear programming involves optimizing a linear objective function, subject to a set of linear inequalities or constraints.

2. **Identifying the Objective Function**:
- The objective function is typically denoted as \( z \) and represents the value we want to maximize or minimize.

3. **Recognizing Constraints**:
- Constraints are inequalities that limit the values of the variables (e.g., \( 2x + 3y \geq 12 \), \( x \leq 10 \), \( y \leq 5 \)). These constraints define the boundaries of the feasible region.

4. **Graphing the Constraints**:
- To visualize the feasible region, we graph the constraints on a coordinate plane (x-y plane). Each inequality divides the plane into two halves, and the feasible region is where all these inequalities overlap.

5. **Defining the Feasible Region**:
- The feasible region is the area where all constraints are satisfied simultaneously. This region includes all possible solutions that meet the criteria set by the constraints.

6. **Conclusion**:
- The area containing all the possible solutions to the problem which are feasible is called the **feasible region**.

### Final Answer:
The area containing all the possible solutions to the problem which are feasible is called the **feasible region**.

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