Define a feasible region in LPP.

In linear programming, the feasible region refers to the set of all possible solutions that satisfy the constraints of the linear programming problem. It is the region in the solution space where all the constraints are simultaneously satisfied.

To define the feasible region, we need to consider the following components:

Decision Variables: These are the variables that we want to determine in the linear programming problem. For example, if we have two variables, x and y, the decision variables would be x and y.

Objective Function: The objective function defines the goal or objective of the linear programming problem, either to maximize or minimize. It is typically a linear equation involving the decision variables. For example, if we want to maximize profit, the objective function could be 3x + 2y.

Constraints: Constraints represent the limitations or restrictions on the decision variables. They are expressed as linear inequalities or equations. For example, x + y ≤ 10 represents a constraint where the sum of x and y should be less than or equal to 10.

The feasible region is determined by the intersection of all the constraints in the problem. It is the set of all values of the decision variables that satisfy all the constraints simultaneously. Graphically, the feasible region is often represented as a bounded or unbounded region in the coordinate plane.

For example, consider a linear programming problem with two variables, x and y, subject to the following constraints:

2x + y ≤ 8
x + 2y ≤ 10
x ≥ 0
y ≥ 0
The feasible region would be the area in the xy-plane that satisfies all the given constraints, which would typically be a polygon or a region bounded by lines.

Note that the feasible region may vary depending on the specific constraints and objective function of the linear programming problem.