The Vertex Method

The Fundamental Concept of Vertex Method

Understand that vertex method is a technique used to solve linear programming problems by examining the vertices of the feasible region.
Know that each vertex of the feasible region represents a potential solution, with the optimal solution being the one that maximizes or minimizes the objective function.

Identify all vertices of the feasible region. This can be done mathematically through interpolation or graphically via plotting.
Substitute each vertex into the objective function. This step will give you a corresponding value for every vertex.
The vertex that yields the highest or lowest output, depending on whether it’s a maximization or minimization problem, is the solution.

Note that the vertex method is precise and gives an exact solution when solving linear programming problems.
Understand that this method can be cumbersome and time-consuming if there are a large number of variables or constraints. It might not be practical for real-world problems that have such complexity.
The method also assumes linearity of constraints and objective functions, which are not always realistic in real-world contexts.

Be proficient in applying the vertex method in a wide range of real-world problems, such as maximizing profit, minimizing cost, or optimizing resource allocation.
Demonstrate the ability to interpret the results and draw conclusions based on the solutions obtained using the vertex method.
Understand how to adjust or alter the constraints or the objective function to reflect changes in the real-world scenarios and observe how these changes affect the optimal solution.

Understand the differences and similarities between the vertex method and other techniques like the simplex method or the graphical method.
Note that each of these methods have their own advantages and limitations. Consider these when choosing the most suitable method to solve a given linear programming problem.