# How to Get Answers of a 2 By 2 Matrix Linear Programming Maximization Problem Without Artificial Variables Using Nickzom Calculator

**Last Updated on February 11, 2024**

Navigating linear programming maximization problems involving 2 by 2 matrices without artificial variables poses a challenge for many. However, understanding the underlying principles and employing strategic techniques can simplify the process significantly. Many students and professionals can do with help from a specialized calculator that helps them solve Matrix Linear Programming Maximization Probelms as well as showing them the workings. This is where Nickzom calculator comes in.

However, before we get to that, let’s explore efficient methods to obtain solutions and optimize decision-making in such scenarios.

According to Google Dictionary, **Linear Programming** is a mathematical technique for maximizing or minimizing a linear function of several variables, such as output or cost.

On the other hand, Wikipedia describes as **L****inear programming** (**LP**, also called **linear optimization**) a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. Linear programming is a special case of mathematical programming (also known as mathematical optimization).

### Solving Linear Programming Maximization with Nickzom Calculator

You might be wondering how possible is it for there to be a calculator that can really solve linear programming calculations and show the workings at the same time. **Nickzom Calculator** does that for you at the very best of all capabilities.

Nickzom Calculator can not only solve a 2 by 2 matrix linear programming problem but can also solve for an m by n matrix problem. At the moment, Nickzom Calculator can handle:

- Maximization Without Artificial Variable(s)
- Minimization Without Artificial Variable(s)

Computations of Linear Programming with artificial variables is on the way and I do promise to inform you once it is integrated into the calculator encyclopedia via this blog.

Nickzom Calculator makes use of **simplex method** to compute the result for linear programming problems. There is an iterative computation of steps to obtain the final result which is when there is no further negative entry in the index/third/**P** row of which a basic solution emerges for x and y variables with all the other variables equal to **0**. At this point, the **optimal solution** and **optimal value** is given.

### Steps in Iterative Simplex Method

The various steps used in the **iterative** simplex method are outlined accordingly:

- Obtain the key column which is the column containing the most negative entry in the index row.
- Obtain the key row by dividing the value in the b column by the entry in the key column, of which the smallest positive ratio determines the key row.
- Divide all entries in the key row by the
**pivot**to reduce the pivot to**unity**(that is 1). - Make use of the main row to work on the remaining rows of the table to reduce the other entries in the key column to zero.
- If there is a presence of negative entry in the index/third/P row.
**Repeat Steps**from Beginning.

The moment you have been waiting for, how can Nickzom Calculator solve this operation. First and Foremost, access Nickzom Calculator – **The Calculator Encyclopedia **via any of these means:

Web – https://www.nickzom.org/calculator-plus

Android (Paid) – https://play.google.com/store/apps/details?id=org.nickzom.nickzomcalculator

Apple (Paid) – https://itunes.apple.com/us/app/nickzom-calculator/id1331162702?mt=8

Proceed to **Calculator Map** under the Engineering Section

Click on **Linear Programming**

Click on **Maximization Without Artificial Variables**

Nickzom Calculator computes for two means of maximization without artificial variable(s), which are:

- Simplex with Two
**Problem Variables**| Two**Inequalities** - Simplex with N
**Problem Variables**| M**Inequalities**

Since the purpose of this post is a 2 by 2 matrix, click on simplex with two problem variables and two inequalities.

Now, enter your values and coefficients accurately just like the image below

All you have to do now, my loving friend is just click on the **Calculate** and Nickzom Calculator works its magic in less than a second and displays for you the result with the complete workings and tutorials. For the purpose of this post, I would display the result in the form of a **video**. Watch and Enjoy!