The Linear Programming Calculator is a free online tool that shows the best optimal solution for the restrictions you provide. However, it is the most effective optimization strategy for obtaining the prime solution for a given objective function with a set of linear limitations. However, in a fraction of a second, our online linear programming calculator tool presents the best optimal solution for the supplied objective functions with the system of linear constraints.

Table of Contents

**Linear Programming Calculator Input**

The inputs of our Linear Programming Calculator are:

- Maximize or Minimize
- Then, the Objective function
- Then, Subject to functions

**Linear Programming Calculator with Steps**

The following is how to use the linear programming calculator:

1st Step: First of all, fill in the goal function and constraints in the appropriate input fields.

2nd Step: Then to get the best solution, click the “Submit” button.

3rd Step: Then in the next window, the best optimal solution and graph will be displayed.

**Linear Programming Calculator Outputs**

The outputs of our Linear Programming Calculator are:

- Input statement
- Then, the Global maximum
- Color plot
- Then, a 3D plot

**What Is Linear Programming?**

In short, linear programming is a method for optimizing a linear objective function under the restrictions of linear equality and linear inequality. However, it has a convex polytope as its possible region, which is a set we define as the junction of a limited number of half-spaces. Meanwhile, we specified each of these by a linear inequality. This polyhedron’s objective function is a real-valued affine (linear) function. However, if there is a location in the polytope where this function has the smallest (or greatest) value, a linear programming approach identifies it.

**Linear Programming Definition **

In short, linear programming is a mathematical strategy for achieving the optimal result inside a mathematical model with linear relationships representing the requirements. It is a form of mathematics programming.

In nature, linear programming is a method for optimizing a linear objective function that has linear equality and inequality limitations. However, this collection contains a convex polytope, which we define as the intersection of a finite number of half-spaces. However, linear inequality specifies each of these. Meanwhile, a real-valued affine function defines the objective function of this polyhedron.

**Linear Program Calculator 3 Variables, Terminologies**

Let’s use the following example to define some Linear Programming terminology.

- Decision Variables:

First of all, the decision variables are the factors that will impact the outcome of my project. They are the final solution for me. However, we must first identify the decision variables to solve any challenge. Meanwhile, my choice variables in the preceding example are the total number of units for A and B, labeled by X and Y, respectively.

- The function of the objective:

We can define this as the goal of decision-making. However, in the example above, the company wants to enhance total profit, Z. As a result, profit is my primary goal.

- Constraints:

However, constraints are limitations or restrictions placed on the decision factors. Moreover, they frequently set a limit on the decision variables’ value. However, this limits the availability of resources in the coming first situation. My limitations are milk and chocolate.

- Non-negativity constraint:

However, the decision variables in all linear programs must always be non-negative. This means that the decision variable should have values that are larger than or equal to 0.

**How to Formulate a Linear Programming Problem in a Linear Programming Calculator?**

Let’s take a look at how to define a Linear Programming problem in general:

- Determine the variables that affect your decision.
- Then, create the goal function.
- Mention the limitations.
- Then, clearly state the non-negativity restriction.
- However, the choice variables, objective function, and restrictions must all be linear functions for a problem to be classified as a linear programming issue.

It’s referred to as a Linear Programming Problem if all the conditions are met.

**Application of Linear Programming Calculator Example **

Datasets | M1 | Then, M2 | M3 | Then, M4 | M5 | Then, M6 | Then, M7 | FLP-M3 |

CAR F92 | 10 | 7 | 9 | 8 | 9.50 | 8 | 7 | 7 |

Then, CAR S91 | 12 | 10 | 11 | 10 | 10 | 10 | 10 | 10 |

Next, EAR F83 | 4 | 2 | 2 | 1.50 | 2 | 3 | 2 | 1.50 |

Then, HEC S92 | 14 | 11 | 10 | 9.50 | 11 | 11 | 11 | 9.55 |

Next, KFU S93 | 12 | 5 | 6 | 5.50 | 7 | 5 | 6 | 5 |

Then, LSE F91 | 5 | 2 | 3 | 2 | 4 | 3 | 3.5 | 2 |

Next, PUR S93 | 110 | 80 | 90 | – | – | – | 87 | 80 |

Then, RYE S93 | 5 | 5 | 5 | 5 | 5.50 | 5 | 5 | 5 |

STA F83 | 31 | 0.50 | 0.70 | 0.80 | 0.90 | 0.55 | 0.50 | 0.50 |

Then, TRE S92 | 3 | 2 | 2 | 2 | 2.50 | 2 | 2 | 2 |

Next, UTA S92 | 10 | 9 | 9.50 | 9 | 9 | 9 | 9 | 9 |

Then, UTE S92 | 2 | 1 | 1 | 1 | 1.20 | 0.90 | 1 | 1 |

Next, YOR F83 | 3 | 2 | 2 | 2 | 2 | 3 | 2 | 2 |

**Linear Programming Calculator Graphical Method**

We can use multiple strategies to solve a linear program. However, we’ll look at the Graphical approach for solving a linear program in this part. Meanwhile, one can solve a two-variable linear program using this method. However, if you just have two choice factors, you should use the graphical method to discover the best solution.

However, defining a set of linear inequalities subject to restrictions is a graphical method. Then we plot the inequalities on an X-Y coordinate plane. Moreover, the intersection region gives us a possible region once we have drawn all of the inequalities on a graph. Meanwhile, the viable region describes the range of possible values for our model. It also provides us with the best solution.

**Linear Programming Calculator with Graph Example**

However, for example, assume a farmer recently purchased a 110-hectare piece of property. Moreover, on that plot of land, he has opted to produce wheat and barley. One might sell the complete wheat and barley crop because of the high quality of the sun and the favorable temperature of the region. However, given the costs, net incomes, and labor requirements shown below, he wants to know how to plant each type in the 110 hectares:

Variety Cost (Price/Hec) | Net Profit (Price/Hec) | Man-days/Hec |

Wheat 100 | 50 | 10 |

Then, Barley 200 | 120 | 30 |

During the planning horizon, the farmer has a budget of RS 10,000 and 1,200 man-days available. However, find the best solution and the best price.

**Solution:**

First of all, we’ll start by developing a linear program to solve this problem.

LP Formulation

### 1st Step

Firstly, determine the variables that affect your decision.

Meanwhile, X is the total area available for producing wheat (in hectares)

However, ‘Y’ is the total area available for growing barley (in hectares)

Then my decision factors are X and Y.

### 2nd Step

Next, create the goal function.

Because one can sell the entire land’s production on the market. However, the farmer’s goal would be to maximize the profit on his entire crop. For both Wheat and Barley, we got a net profit. Meanwhile, for each hectare of Wheat and RS120 for each hectare of Barley, the farmer makes a net profit of RS50.

Then, Max Z = 50X + 120Y is our objective function (provided by Z).

### 3rd Step

Constraints are written

- Assume the farmer has a total budget of RS10,000. We are also provided with the cost of producing Wheat and Barley per hectare. We have a limit on how much the farmer can spend in total. As a result, our equation is:

Then, 100X + 200Y ≤ 1000. The next limitation is a maximum limit on the total number of man-days available for the planning horizon. However, there are 1200 man-days available in total. Moreover, we are given the man-days per hectare for Wheat and Barley in the table.

10X + 30Y ≤ 1200

- Then the total area available for plantations is the third limitation. However, the entire amount of land available is 110 hectares. As a result, the equation becomes X + Y ≤ 110.

### 4th Step

The restriction on non-negativity

X and Y will have values that are larger than or equal to 0. This is self-explanatory.

X ≥ 0, Y ≥ 0

Then, we developed our linear program. It’s past time to find a solution.

Then, using the graphical method to solve an LP

However, we already know that X, Y ≥ 0. Similarly, only the first quadrant will be considered.

First, I’ll simplify all of the equations before plotting the graph for the above equations.

Then, we can write100X + 200Y ≤ 10,000 as X + 2Y ≤ 100 by dividing by 100.

We can also write 10X + 30Y ≤ 1200 as X + 3Y ≤ 120 by dividing by 10.

Hence, the third equation is in its simplified form, X + Y ≤ 110.

Moreover, plot the first two lines in the first quadrant on a graph (like shown below)

However, at the point of the junction where the budget and man-days restrictions are active, the best possible solution is found. However, this means that the crossing of the equations X + 2Y ≤ 100 and X + 3Y ≤ 120 yields the best answer.

Hence, the values for X and Y that result in the best solution are as follows: (60,20).

However, wheat and Barley should be grown on 60 hectares and 20 hectares of land, respectively, to optimize profit.

Hence, the company’s maximum profit will be: Max Z = 50 * (60) + 120 * (20) = RS5400.

**Linear Programming Calculator Simplex Method**

- Set the scene for the issue. To put it another way, write down the objective function as well as the inequality restrictions.
- Then make equations out of the inequalities. However, we represent each inequality by a single slack variable.
- Then create the first simplex tableau. However, the objective function should be written in the bottom row.
- Then the pivot column is identified by the most negative entry in the bottom row.
- Determine the quotients. Meanwhile, a row is identified by the least quotient. However, the pivot element is the element at the intersection of the column identified in step 4 and the row identified in this step. Then divide the far right column by the indicated column in step 4 to get the quotients. Meanwhile, the quotient with a denominator of zero, a negative value, or a zero in the numerator is ignored.
- Then, make all other entries in this column zero by pivoting. However, this is accomplished in the same manner as the Gauss-Jordan approach.
- We’re done when there are no more negative entries in the bottom row; otherwise, we’ll start over at step 4.
- Then, read your responses aloud. However, using the columns with 1 and 0s, get the variables. All of the other variables are set to zero. Meanwhile, in the bottom right-hand corner, you’ll find the maximum value you’re looking for.

**Linear Program Calculator Max and Min**

**An Example**:

However, consider the problem below, which has an equality constraint: Maximization 3x + 2y + z,

Submit to: 4x + 2y + 3z = 12

Where x + z ≥ 1

x, y, and z ≥ 0.

When two inequality restrictions are combined, we get the following equivalent problem:

Maximization 3x + 2y + z

Subject to:

4x + 2y + 3z ≤ 24

Then, 4x + 2y + 3z ≥ 24

x + z ≥ 1

x, y, and z ≥ 0.

Fill in your usual LP problem in the table below, then press the “Calculate” button.

**Solve Linear Program Calculator Opensolver**

In fact, a linear program can have anywhere from 30 to 1000 variables, making it very hard to solve graphically or algebraically. Meanwhile, Opensolver is commonly used by businesses to solve these real-world issues. However, I’ll walk you through how to use it to solve a linear program.

However, it is free to use. It’s a more advanced version of Excel’s built-in Solver.

**Linear Programming Application**

- In a variety of sectors, we apply linear programming and optimization. We also use Linear programming widely in the manufacturing and service industries. However, we’ll look at the numerous applications of linear programming in this part.
- Industries also use linear programming in the manufacturing industry to analyze supply chain activities. Their goal is to maximize efficiency while keeping operating costs to a minimum. However, the factory can restructure its storage architecture, modify its personnel, and decrease bottlenecks based on the linear programming model’s recommendations. However, Cequent, a US-based corporation, has a modest Warehouse case study; watch the video for a better idea.
- In organized retail, linear programming is also utilized to optimize shelf space. Because the quantity of products on the market has grown by leaps and bounds, it’s critical to know what the customer wants. However, Walmart, Hypercity, Reliance, Big Bazaar, and other retailers employ optimization greatly. Meanwhile, the products in the store are slowly placed to accommodate the purchasing habits of the customers. However, the goal is to make it simple for customers to find and purchase the proper products. We can limit this by factors such as shelf space, product variety, and so on.
- Delivery Routes can also benefit from optimization. Moreover, this is a variation on the well-known problem of the travelling agent. However, for several salesmen travelling to multiple places, the service business employs optimization to identify the optimal path. However, companies like FedEx, Amazon, and others pick delivery routes using clustering and greedy algorithms. In short, the goal is to minimize the system cost and time.
- However, machine learning makes use of optimizations as well. Also, supervised Learning focuses on linear programming concepts. Meanwhile, labeled input data can predict values from unknown test data.

**Some Frequently Asked Questions about Linear Programming Calculator (FAQs)**

#### Is linear programming easy?

In short, linear programming is a technique for solving problems that we restrict in some way. However, it is the process of maximizing or minimizing linear functions under restrictions of a linear inequality. Moreover, the challenge of solving linear programming is thought to be the simplest.

#### Is calculus linear programming?

However, the difficult part of linear programming challenges is figuring out what the boundary looks like. By definition, we use linear programming to solve problems when the function that we need to minimize is linear, therefore all calculus can tell us (and it can tell us rapidly) is that there are no extrema in the domain’s interior.

#### What is linear programming with examples?

In short, a company that must dedicate its time and money to creating two different goods is the most typical example of a linear programming problem. The items demand varying quantities of time and money, both of which are often scarce resources, and they sell at varying costs.

#### How is linear programming used in real life?

Linear programming is a skill for optimizing processes while attaching to particular limitations. However, we use it to improve the efficiency and cost-effectiveness of processes. Similarly, food and agriculture, engineering, transportation, manufacturing, and energy are some of the domains where linear programming can be used.

#### How is the simplex method used in linear programming?

We need to follow the following steps to solve a linear programming model using the Simplex method:

- This is the standard format.
- Then we introduce Slack variables.
- Next, we put together the scene.
- Then, variables are in pivot tables.
- Then, a new tableau is being created.
- Performing a check for optimality.
- Then, determine the best values.