Question

Which of the following statements is true with respect to the optimal solution of an LP problem?

1.Every LP problem has an optimal solution

2.Optimal solution of an LP problem always occurs at an extreme point

3.At optimal solution all resources are completely used

4.If an optimal solution exists, there will always be at least one at a corner

Answer 1

If an optimal solution exists, there will always be at least one at a corner

Step-by-step explanation:

Every LP problem has an optimal solution  : not necessary

There can be constraint Such that there is no solution meeting all constraints

Optimal solution of an LP problem always occurs at an extreme point

- True but it can be at other points too

At optimal solution all resources are completely used -

Not Necessary  

If an optimal solution exists, there will always be at least one at a corner

- True

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Answer 2

The statement true with respect to LP is d) If an optimal solution exists, there will always be at least one at the corner.

• The feasible solution with the largest objective function value for a maximization problem is an optimal solution to a linear program.
• An LP problem will always have one optimal or more than one optimal solution at the corner but not exactly two solutions.
• The corner points exist only in the feasible area at a vertex. When an optimal solution to a linear programming problem occurs, it can occur at one or more corner points, or between two corner points on a line segment.