In linear programming, what is the feasible region?

In linear programming, what is the feasible region?

• A. The region where the objective has maximum value
• B. The region where the objective has minimum value
• C. The boundary of the feasible region
• D. The set of all points that satisfy every constraint

Answer: (D)

The feasible region is the set of all values of the decision variables that satisfy every constraint. It arises from intersecting all constraint half-spaces (and any equalities), including nonnegativity, so it forms a convex region in the decision-variable space. Within this region, some points lie strictly inside (all inequalities are strict) and others lie on the boundary where constraints are tight. The objective function is evaluated over this region to find a maximum or minimum, and in linear problems those optima typically occur at boundary points or vertices, but the region itself is just the collection of feasible points, not the location of the optimum. The other options describe where the optimum might be or focus only on the boundary, which doesn’t define the feasible region.

The feasible region is the set of all values of the decision variables that satisfy every constraint. It arises from intersecting all constraint half-spaces (and any equalities), including nonnegativity, so it forms a convex region in the decision-variable space. Within this region, some points lie strictly inside (all inequalities are strict) and others lie on the boundary where constraints are tight. The objective function is evaluated over this region to find a maximum or minimum, and in linear problems those optima typically occur at boundary points or vertices, but the region itself is just the collection of feasible points, not the location of the optimum. The other options describe where the optimum might be or focus only on the boundary, which doesn’t define the feasible region.