Discussion
Which of the following statements is true with respect to the optimal solution of an LP problem ?
Answer: C
The true statement is if an optimal solution exists, at least one optimal solution lies at a corner of the feasible set.
This is the fundamental theorem of linear programming: if the feasible region has extreme points and the objective attains its optimum, it attains it at some extreme point (basic feasible solution). That is why the simplex method searches only the corners.
The others fail. An LP may be infeasible or unbounded, so not every LP has an optimum. The optimum need not occur 'only' at extreme points: with alternative optima, every point of an edge between two optimal corners is optimal (as in Q9). And a feasible solution is optimal only by coincidence.
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