Start from non‑negativity (all variables ≥ 0), then apply each constraint one by one — keep only the area that satisfies all of them so far. The feasible region is simply the overlap of every constraint’s allowed space. Adding more constraints can only shrink or leave it unchanged, never expand it. If no overlap remains, the problem is infeasible. For many constraints, use the Simplex method instead of graphing.

When a Linear Programming problem has many constraints, the feasible region is determined by finding the area where all constraints are satisfied at the same time. Each constraint creates a boundary, and the overlapping area that satisfies every constraint, including non-negativity conditions, is the feasible region. With many constraints, software such as POM-QM can help identify and analyze the feasible region more efficiently.

You can determine the feasible region by systematically checking the intersection of all constraints and identifying the points that satisfy every constraint. With many constraints, tools like Excel Solver or LP software can help identify the feasible region efficiently.