Q.The feasible region of an LPP is the set of all points that: (A) satisfy at least one constraint (B) satisfy the objective function (C) satisfy all the constraints and the non-negativity restrictions simultaneously (D) lie on the boundary lines only

Recall the definition of the feasible region.

The feasible region is the common overlap of every constraint half-plane.

The feasible region is, by definition, the set of all points $(x,y)$ that satisfy every constraint and the non-negativity restrictions $x\ge0,\ y\ge0$ at the same time — the common (overlapping) region of all the half-planes.

Why the other options are wrong:

• (A) Satisfying at least one constraint is far too weak — a feasible point must satisfy all of them.
• (B) The objective function is what we optimise over the region; a point does not "satisfy" it, and it does not define the region.
• (D) The region is a solid area, not just its boundary lines; interior points are feasible too.

Only (C) is the correct definition.

Check (independent verification): in Worked Example 5, $(2,2)$ was feasible because it satisfied both $x+3y\ge3$ and $x+y\ge2$ (and $x,y\ge0$) — satisfying only one would not have placed it in the region.

Choosing (A): a point that meets only one constraint but violates another is infeasible. Feasibility requires every constraint to hold together.