Graphical method can only solve 2 variables while Simplex method can solve 2 or more variables.

Simplex Method is giving a one only optimal solution and it is the most profitable way of choosing a decision, but in the other way of linear programming the Graphical Method showing all the option that constraints creates, it can 2 or more optimal solution for the problem.

For graphical method, it shows you the overview of the problem and also the intersection of all constraints that would help you to find the answer, while in Simplex method it shows you the overlay structure of all the variables and your constraints even though it has complex for me it is more accurate than the graphical.

Graphical Method suitable for problems with few variables and constraints while Simplex Method Suitable for problems with multiple variables and constraint.

Graphical method can only solve 2 variables and applicable tru graphs while the simplex method use more than 2 variables and it's not applicable tru graphs 

The Simplex method can solve two variables or more, however the Graphical method can only solve two variables

I find the Simplex Method to be more precise and suitable for handling problems with two or more variables, whereas the Graphical Method is straightforward and provides quick answers but is limited to solving problems with just two variables.

The Simplex Method is more accurate for me and it can solve with two or more variables on the other hand Graphical Method is straight to the point to answer or clear but it can be solve by 2 variables only

Graphical method assess all corner points while simplex solving linear  programming by hand

Graphical Method:

Finding the value of the goal function at each vertex in the graphical technique is necessary to determine the viable zone.

When we have to determine the answer of two decision variables, we prefer the graphical method.

Simplex Method:

In the simplex method, we identify the best value at the conclusion to obtain the workable region.

When we need to determine the answer of more than two choice variables, we prefer the simplex technique.

The graphical method is only useful if you want to solve a 2D model, i.e., a model with only 2 decision variables. It doesn’t have much practical use outside of the classroom, when students are first introduced to LP models.

The Simplex method is an algorithm originally proposed by George Dantzig, and is applicable for solving LPs of any size (subject to computing resources, of course). It begins by first finding an extreme (corner) point of the feasible region, and it continues searching for extreme points along directions of improvement until certain optimality conditions are satisfied, namely primal feasibility, dual feasibility, and complementary slackness.

Simplex method was use in order to attain to multiple variable in a given problem or set while the graphical is only applicable for atleast 2 variables. Both of them has perks on their usage base on the given problem 

Simplex method can solve two or more variables, While Graphical method can only solve two variables.

Although graphical methods are easier, they are not necessarily suitable for all problem types. The simplex approach contains more steps but solves a wider range of problems.