Discussion
In the graphical method of a linear programming problem, the optimal solution lies
Answer: B
The optimal solution lies at a corner point of the feasible region.
The fundamental theorem of linear programming says that if a linear objective has an optimum over a bounded (or suitably unbounded) convex feasible region, it occurs at a corner point (vertex). That is why the corner-point method evaluates the objective only at the vertices.
The centre of the region is never singled out; the origin or a point on the \(x\)-axis is optimal only when it happens to be a vertex; and the objective function being zero has nothing to do with optimality.
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