Feasible Solution in Linear Programming Problem

A linear programming problem (LPP) involves optimizing an objective function while satisfying a set of linear constraints. The feasible solution of an LPP refers to a solution that satisfies all the constraints of the problem. In other words, it is a solution that falls within the feasible region defined by the constraints.

The feasible region is the intersection of all feasible solutions. It is a geometric representation of all the possible values that the decision variables can take while satisfying the constraints. The feasible region is typically represented graphically as a convex polygon or polyhedron in two or three dimensions, respectively.

Quadrants in Cartesian Coordinate System

In a Cartesian coordinate system, the plane is divided into four quadrants. These quadrants are numbered from 1 to 4, starting from the top right quadrant and moving counter-clockwise.

- Quadrant 1: The first quadrant is located in the top right portion of the plane, where both the x and y coordinates are positive.
- Quadrant 2: The second quadrant is located in the top left portion of the plane, where the x coordinate is negative and the y coordinate is positive.
- Quadrant 3: The third quadrant is located in the bottom left portion of the plane, where both the x and y coordinates are negative.
- Quadrant 4: The fourth quadrant is located in the bottom right portion of the plane, where the x coordinate is positive and the y coordinate is negative.

Feasible Solution and Quadrants

Now, coming back to the question, it states that the feasible solution of an LPP belongs to the first quadrant only (option C).

This means that in the feasible region of the LPP, all the feasible solutions lie in the first quadrant. In other words, the values of the decision variables that satisfy the constraints of the problem are positive.

This can be visualized by considering a two-variable LPP. In this case, the feasible region would be a convex polygon in the first quadrant. Any feasible solution within this region would have positive values for both variables.

It is important to note that this statement is specific to the given question and may not hold true for all LPPs. The feasible region and the location of feasible solutions can vary depending on the specific constraints and objective function of the problem.

So, in conclusion, the feasible solution of an LPP can belong to different quadrants depending on the problem, but in this specific case, it belongs only to the first quadrant (option C).