The **Big M method** is one of the mandatory learning techniques for operations research students and often creates difficulties for them because of the calculations involved. To help you better understand this method, we have developed an online calculator to solve linear programming problems by the Big M method. This tool has the same operation and aesthetics very similar to our online application of the two-phase simplex method.

## Big M Method Calculator - Free Version

The Big M online calculator, in its free version, shows us the tables for each of the iterations needed to reach the final solution. However, if you want to learn more about how each number is obtained in the tables, we suggest you check the pro version of our calculator:

### Advanced Functions of the Big M Method Online Calculator

To solve linear programming exercises with the method of the big M, we must apply the simplex algorithm. This is why we have developed a calculator, for all our users with membership, which gives you a detailed explanation of how the algorithm is applied in each of the rows of the table and how to obtain the corresponding values. For this purpose we have included the following functionalities:

- You can solve exercises with up to 20 variables and 50 constraints.
- Analysis of how to determine the optimality condition.
- Explanation of the criteria to establish the feasibility condition.
- Explanation of the calculations performed to obtain the vector of reduced costs, the pivot row and the other rows of the table.
- Analysis of special cases such as unbounded and infeasible solutions.

You can find complete examples of how the application works in this link.

## How to use the Big M Method Calculator

To use our application, you must perform the following steps:

- Enter the number of variables and constraints of the problem.
- Select the type of problem:
**maximize**or**minimize**. - Enter the coefficients in the objective function and the constraints. You can enter negative numbers, fractions, and decimals (with point).
- Click on “Solve”.
- The online calculator will adapt the entered values to the standard form of the
**simplex algorithm**and create the first table. - You will be able to visualize the tables calculated for each of the iterations of the Big M method. If you use the membership version, you will be able to see step by step calculations of each table value in each of the iterations, as well as an explanation of the optimality and feasibility condition and finally the optimal solution.

### Example:

Below we show some reference images of the step by step and the result of the following example:

The following problem is required to be minimized:

Objective Function Z = 3X_{1} + 2X_{2}.

Subject to the following constraints

2X_{1} + X_{2} ≥ 18

2X_{1} + 3X_{2} ≥ 42

X_{1}, X_{2} ≥ 0

### Solution:

First we enter the number of variables and constraints:

We record the coefficients of the objective function and the constraints:

By clicking on Solve we will see the details of the calculation. Below we show some parts as an example:

Iterations in the pivot row:

And finally the result of the exercise:

It is important to emphasize that the **Big M method** is used to solve problems with constraints with equal and greater or equal signs. These types of constraints will add artificial variables to the standard linear programming model. If the problem only has less or equal sign constraints, the calculator will solve it with the traditional simplex method. In any case, our tool can solve any type of problem, be it minimization and/or maximization.

We remind you that as part of our membership, you will also have access to our calculator for the two-phase method and the graphical method of linear programming.

## Final reflection

Having a software tool that solves the **Big M method** step by step is a “Life Hack” that you should not miss, to increase your productivity, your learning and above all your grades.

If you have questions about it or find an error in our application, we will appreciate if you can write to us on our contact page.