Discussion
Which of the following statement/s is/are true for an LP problem ?
(I) Every feasible solution is a basic feasible solution.
(II) If there is a feasible solution, then there is a basic feasible solution.
Answer: B
The answer is only (II) is true.
(II) is part of the fundamental theorem of linear programming: if a standard-form LP has a feasible solution, it has a basic feasible solution (and if it has an optimal solution, it has an optimal basic feasible solution).
(I) is false: basic feasible solutions are the vertices of the feasible region, while points in the interior or along an edge are feasible but not basic. For example, with \(x_{1} + x_{2} \le 2\), the point (0.5, 0.5) is feasible but has no zero among the decision and slack variables that a basic solution in two dimensions would need.
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