By identifying the feasible region, you narrow down the search space for the optimal solution and ensure that the solution you find satisfies all the problem's constraints. It's a fundamental concept in linear programming that plays a critical role in solving optimization problems efficiently and accurately.

Because these constraints typically include inequalities representing limits on resources, capacities, or requirements.

The feasible region in the graphical method of optimization is the area on a graph that represents all possible solutions to a linear programming problem that satisfy the given constraints. It is formed by the intersection of the constraint boundaries and visually identifies the set of solutions that are valid based on the restrictions imposed. Determining the feasible region is crucial because it helps to ensure that any solution derived from the optimization process is realistic and implementable in the real world, and it allows analysts to identify the optimal solution—typically located at one of the vertices of the feasible region—where the objective function achieves its best value.