What are the differences between the simplex method and the graphical method in linear programming?

What are the differences between the simplex method and the graphical method in linear programming?

The simplex method is an algorithm for solving linear programming problems, especially when there are more than two variables. In contrast, the graphical method is a visual approach used primarily for problems with two variables, allowing you to see feasible regions and optimal solutions on a graph.

Can you explain how the graphical method works?

Sure! The graphical method involves plotting the constraints of a linear programming problem on a graph. The feasible region is formed by the intersection of these constraints, and the optimal solution is found at one of the vertices of this region.

When should I use the simplex method instead of the graphical method?

You should use the simplex method when dealing with problems that have three or more variables, as the graphical method becomes impractical. The simplex method is more efficient for larger problems.

Are there any limitations to the graphical method?

Yes, the graphical method is limited to two-variable problems and can be less precise for complex constraints. It also doesn't handle integer programming.