# Linear Programming Problems

Linear programming is a mathematical technique used by the majority of software developers for solving real-life business problems. It helps in decision-making using different techniques to find a solution for the problem. It mainly helps business owners to make the best and most effective use of the available resources to earn profit.

A linear programming problem is given in the form of a linear function and it has to be optimized by using different types of constraints. In a linear programming problem, there are two linear variables.  A function is created with the two linear variables and it is called the objective function.

Linear programming is very useful in solving many day-to-day problems. Hence, it has been integrated into software programming to provide effective and quick solutions. The skills and knowledge required to integrate these can be acquired by enrolling in the best Software programming course.

Let’s understand it in detail.

## Data Science & Linear Programming

Data science is growing rapidly and the most important application of data science is optimization. Companies are looking for skilled data scientists to work on their projects because they need to work on optimizing things. This helps the companies in getting the most optimum results by using the available resources. In day-to-day life and different types of businesses, optimization problems are seen. Some problems are easy to solve and some are complex. Linear programming programs also come under optimization problems. Linear programming is an important concept studied in the field of data science. If you want to excel in the field of data science you must learn the concept of linear programming.

Linear programming and optimization are closely related to each other. It is an important concept used in data science. Linear programming helps in optimization because it helps in finding a solution for the most complex problems. A person can make simple assumptions for solving a complex problem using the techniques of linear programming. If you are working as a data scientist you must know the tools used in linear programming because you will come across different situations when you will use linear programming tools. In data science and machine learning, linear programming is used extensively.

## How does Linear Programming Resolve the Problems in Different Fields?

Linear programming can be used in solving complex problems in different fields. A person has to create inequalities and make proper graphs for solving problems using linear programming tools. Linear programming tools can be applied in different fields for solving complex problems. Some of the fields in which linear programming techniques can be applied include the following:

• Marketing of Products & Services

Linear programming is an important tool that helps in the marketing of products and services. It helps companies to analyze the targeted audience covered during the advertising of the products. They work based on different constraints such as advertising budget, available resources for advertising, etc. The company can also choose the shortest route for the salesmen to reach customers easily and quickly by using linear programming. The transport head of the company can also use linear programming for finding the best schedule for transporting the materials and products from one location to another to reduce transportation costs.

• Financial Sector

Linear programming is also very useful in solving complex problems of financial institutions. Banks, financial firms, and insurance firms can use linear programming for finding the best investment schedule for the customers to enhance the maximum profit on investment. This will help them to provide the best services to the customers.

• Food & Agriculture Industry

Farmers can also make use of linear programming for determining the best crops to grow. They can also find out the quantity of a particular variety of crops to be produced for increasing the profit. They can also use linear programming techniques for finding the type of crops that can be produced by using less expenditure to earn maximum profit.

• Making an Inventory

Companies involved in supplying raw materials to other organizations can also use linear programming. They can use linear programming for finding the best solution to reduce the cost of inventory depending on the demand and space. Demand and space can be used as problem constraints for finding the optimum solution.

• Management of Human Resource

Human resource managers can use linear programming for solving the problems associated with the selection, recruitment, training, and deployment of workers in an organization for different departments. They can use linear programming for finding the minimum number of workers required for different departments and different shifts to meet the schedule of production. Thus, linear programming can help in using the minimum number of employees for increasing the production of a company.

## Problems in Linear Programming

Linear programming is used in different fields for getting the best results or outcomes for the available information. The developers create a program for linear programming to resolve the time-taking issues with precision and in a short span of time.

Let’s discuss the integral working of linear programming and how the software uses mathematical functions to efficiently solve problems.

Problems Related to Manufacturing: Manufacturing problems include problems related to business or industry. In a business, the owner wants to produce a larger amount of products by using fewer men’s power, more working hours, and using labor at lower wages to get the maximum profit.

Example –

A company produces air conditioners, one is window AC and the other is split AC. The available resources can be used for producing 200 sets in a week. The cost of producing a window AC is Rs 2500 and the cost of producing a split AC is Rs. 3500. The company cannot spend more than Rs. 60500 in a week producing air conditioners. If a company can earn a profit of Rs. 500 per window AC and Rs. 600 for producing a split AC, how many windows and split ACs does the company produce to earn the maximum benefit? Solve the problem using linear programming.

This problem can be solved easily using the techniques of linear programming and can help a company in earning the maximum profit by using the available resources.

Similarly, linear programming can also be used for solving diet issues. A person can plan a diet including the necessary nutrients and reducing the cost of the foods used for getting the nutrients.

Linear programming is also used in solving problems related to transportation. A person can check the transportation schedule and can choose the best and cheapest mode of transport for delivering the products from one place to another.

Linear programming is mainly used for finding the best possible solution for a given problem. The outcome of the problem can help in decision-making and improving the methods for getting the best results.

## How do I Formulate Problems of Linear Programming?

If you want to use the techniques of linear programming in real life you must know how to formulate the problems of linear programming. For example, if you are a businessman and produce only two types of ice-creams A and B and you need two different types of resources M and N for making ice creams. The requirements for making ice-creams include-

One hundred pieces of type A ice-creams need one kg of resource M and three kg of resource N.

One hundred pieces of type B ice-creams need one kg of resource M and two kg of resource N.

You have five units of resource M and 12 units of resource N. The profit on the sale of ice-creams is-

Rs. 6 on selling one piece of type A ice cream and Rs. 5 on selling one piece of type B ice cream.

How many units of each ice cream will you produce to enhance your profit to the maximum?

Solution-

The linear programming problem can be represented in the following way:

X= 6a + 5b, X is the total profit and a is the number of Type-A ice creams, and b is the number of type B ice creams. We have to enhance the value of X.

The company will try to produce as many pieces of ice cream as possible but the company has limited resources. Thus, the availability of limited resources is a constraint.

Thus, it is a linear programming problem and you can make similar linear programming problems in day-to-day life to find solutions for complex problems.

## Steps For Making Problems of Linear Programming

A linear programming problem must have the features listed below. These help the software developers understand the basics of the given real-time LP problems and resolve them with their codings.

If you want to make a problem with linear programming, you should go through the following steps:

• Choose the decision variables
• Select the objective functions
• Find out the constraints in the problem
• Find the non-negative restriction of the problem

You must keep the above things in mind when you are trying to solve a linear programming problem.

## Conclusion

Linear programming problems have a vast usage. This is an important concept applied to our day-to-day life problems. Businesses, transportation, agriculture, health industry, financial industry, etc. are using linear programming techniques for finding solutions to complex problems.

Data scientists use linear programming for making complex problems easy and simple. Optimization is the main concept used in linear programming that helps in finding the optimum solution for the given problem by using a lesser number of resources. Thus, anyone who wants to learn linear programming can join a software programming course to become proficient in linear programming and other programming techniques.

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