The common region determined by all the linear constraints of a LPP is called the . . . . . region

Options

A. bounded
B. unbounded
C. feasible
D. concave

Answer

To solve the question, we need to identify the term that describes the common region determined by all the linear constraints of a Linear Programming Problem (LPP). Let's break it down step by step:

### Step 1: Understand Linear Programming Problem (LPP)
A Linear Programming Problem involves maximizing or minimizing a linear objective function subject to a set of linear constraints. These constraints can be represented graphically.

**Hint:** Remember that LPP involves constraints that can be represented as lines on a graph.

### Step 2: Graphical Representation of Constraints
When we graph the constraints of an LPP, each constraint divides the plane into two regions: one that satisfies the constraint and one that does not. The area where all constraints overlap is what we are looking for.

**Hint:** Visualizing the constraints on a graph helps in understanding the regions they create.

### Step 3: Identify the Common Region
The region where all the constraints overlap is crucial because it represents all the possible solutions that satisfy all the constraints simultaneously. This region is bounded by the lines representing the constraints.

**Hint:** Think about what it means for a region to satisfy multiple conditions at once.

### Step 4: Terminology
The common region determined by all the linear constraints is specifically referred to as the "feasible region." This is the area where all the constraints are satisfied.

**Hint:** The term "feasible" indicates that the solutions within this region are valid according to the constraints.

### Conclusion
Based on the analysis, the answer to the question is that the common region determined by all the linear constraints of a LPP is called the **feasible region**.

**Final Answer:** The common region determined by all the linear constraints of an LPP is called the **feasible region**.