Linear Algebra (Linear Programming) Feasible solutions and extreme points.

In summary, the conversation is discussing the concept of feasible solutions that are not basic or extreme points. The participants are trying to determine if these types of solutions are always the same. It is suggested that the textbook may have definitions for these terms that can help clarify the difference.
  • #1
Roni1985
201
0

Homework Statement



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(c) Find a feasible solution that is not basic.
(d) Find a feasible solution that is not an extreme point: justify your
answer by using the definition of extreme point.


Homework Equations





The Attempt at a Solution



The whole question is not that important because it's kind of a general question.
aren't they the same questions?
if a solution is feasible and not basic, it's a feasible solution that is not an extreme point.
Isn't it always true?
 
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  • #2
Your textbook should have definitions for all of these terms. If you still are not sure, post the definitions and we'll see if we can sort this out.
 

1. What is linear algebra and how is it related to linear programming?

Linear algebra is a branch of mathematics that deals with linear equations and their representations using matrices and vectors. It is closely related to linear programming, which is a method for optimizing a linear objective function subject to linear constraints.

2. What are feasible solutions in linear programming?

Feasible solutions in linear programming refer to the set of values for the decision variables that satisfy all the constraints of the problem. These solutions lie within the feasible region, which is the intersection of all the constraints.

3. What are extreme points in linear programming?

Extreme points, also known as extreme vertices, are the corner points of the feasible region in a linear programming problem. These points are the intersection of two or more constraints and represent the most extreme values for the decision variables.

4. How do you find feasible solutions and extreme points in a linear programming problem?

To find feasible solutions and extreme points in a linear programming problem, you can use a graphical method or an algebraic method. In the graphical method, you plot the constraints and the objective function on a graph and find the intersection points. In the algebraic method, you use the simplex algorithm to find the optimal solution, which will also reveal the feasible solutions and extreme points.

5. What are some real-world applications of linear programming?

Linear programming has many real-world applications, including production planning, resource allocation, transportation and logistics, financial planning, and portfolio optimization. It is also used in marketing, supply chain management, and even sports analytics to make optimal decisions and maximize efficiency.

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