What Do You Mean By Binding Constraint in Linear Programming

Do you know what is Binding Constraint in linear programming? Have you ever thought about what can be the Binding Constraint in linear programming? Let’s gain some knowledge about the binding constraint in linear programming.

But before we start getting knowledge about it, let us first think about the process from the example of our daily life. Before going in-depth about this topic let’s understand the process with an example.

 

What is Binding Constraint? Get To Know With Example

 

Suppose, you want to start a business. But you can’t able to find out which business will be better for you. You want to open a bookshop. But as well you are thinking to open a garment shop also. What will you do in such cases?

You will first gather some knowledge about both businesses. then you find out at which business you will get a more profit. You have to also think about which business can run in all sessions. All these things you need to think about before starting any business.

The same thing goes for the binding constraint in linear programming. Linear programming helps to find out such solutions in a mathematical way. And it is quite accurate. For getting accurate solutions, there are many types also.

We will first know what is linear programming. Then we have to know how many constraints in linear programming. At last, we will see what is binding constraint in linear programming.

Let us know about them one by one briefly.

 

What Is Linear Programming? Read Below

 

Linear programming is a special mathematical method. This helps to gain some important details about any business model. It helps to optimize the solution. This means it helps to compare & optimize the problems. It helps to find out the problems related to the businesses. Like it can able to find out the maximum profit. Or it can help to find out the minimum cost required for certain work. It works on linear equations.

In linear programming, there are some constraints provided. Based on it, we have to perform operations. We have to find out the maximization or minimization. Depending upon the task, the constraints may get changed. With the help of both constraints; we can find out the feasible regions in the graph. This helps to understand the profit or loss in a better way. Linear programming is also known as linear optimization.

 

What Are The Types Of Constraints In Linear Programming?

 

After getting knowledge about linear programming, it is now time to find out the answer to how many constraints in linear programming. Depending upon their relationship with the optimal solution, there are mainly two constraints in linear programming. But also, there are other types of constraint is present. it is related to the feasible region of the graph. Let us make a list of the available constraints.

1. Binding Constraints: It is related to the optimal solutions. With the change of the optimal solution, inequality arises.
2. Non-Binding Constraints: It is also related to optimal solutions. With the change of optimal solution, the inequality remains the same.
3. Redundant Constraints: It is a constraint that has no relation with the optimal solution. It is related to the feasible region. This constraint has no contribution to developing the feasible region. Such types of constraints are known as a redundant constraints.

But here, our goal is to discuss only the binding constraints in linear programming. Let us now get the answer to the question of what is binding constraints in linear programming.

 

What Do You Mean By Binding Constraint In Linear Programming?

 

Binding constraint in linear programming is a special type of programming. It operates inequality with optimal solutions. There are mainly two constraints present in any problem. Binding constraint in linear programming is one of them. It is an equation in linear programming which satisfied the optimal solution. With the help of optimal solutions, it can get unique values. These values help to find out which constraint is binding.

Does it seem quite difficult to understand? Let us take one example to better understand the topic.

Suppose, a question is provided like: Maximize Z=40x₁ + 35x₂ profit. Subject to 2x₁ + 3x₂ ≤ 60 (Raw Material Constraint) & 4x₁ + 3x₂ ≤ 96 (Labor Hour Constraint). The range is x₁ , x₂ ≥ 0,

Here, our goal is to find out which constraint is the binding constraint in linear programming. So, here it is not needed to discuss the way to find out the maximization.

So, after calculating the maximization, we have the graph. We have plotted the graph below.

 

 

From the graph it is depicted that the values are the x₁ = 18 & x₂ = 8. These values will provide the optimal solution to the problem.

Now, we will take each of the constraints one by one. There we need to put those values. Now, we need to check are the left-hand side & the right-hand side are the same or not. If they are the same, means the constraint is binding. If they are not equal, means they are not a binding constraint.

Let us check for the first one: 2x₁ + 3x₂ = 60 (It should be)

So, the first constraint is the binding constraint in linear programming. As the left-hand side & the right-hand side are equal to each other.

Let us check for the second one: 4x₁ + 3x₂ = 96 (It should be)

So, the second constraint is also the binding constraint in linear programming. The left-hand side & the right-hand side are equal to each other in this case also.

In linear programming, these constraints are binding constraints.  In some cases, one binding may also be a non-binding constraint.

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Conclusion:

 

As we saw the binding constraint in linear programming is very important.

We should always remember what is binding constraints in linear programming. This will help a lot in the future.

How many constraints in linear programming is a very important question to think about it.  Thinking about this will help us to understand the other constraints better.

So, hope you have liked this piece of article. Share your thoughts in the comments section and let us know if we can improve more.

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