How to do linear programming in management? Why is it important to implement this? These are some of the questions we will tackle.

## What Is Linear Programming To Management?

Linear programming is not just a mathematical technique. But it is also the method used by managers to solve problems.

Linear programming is a mathematical optimization technique that allows us to maximize. Also, minimize a linear objective function while satisfying constraints of the problem.

A linear programming problem is a linear objective function with linear constraints. So this means that the objective function and the constraints are all linear equations and inequalities.

## Linear Programming Solving Problems In Management

Some of the most common problems in management can be solved using linear programming. But some of them require modifications to make them linear. Some examples are:

## Shopping/Retail:

How much of each product should be bought? Minimum total cost is a key factor here. It can be used in any retail business – grocery, clothing, etc.

## Warehouse:

How many items should be stored? They must be able to fit in the warehouse, so this will affect the solution.

## Transportation:

It is one of the most common problems for managers. How to maximize profit when transporting several products?

You have to transport all objects, but you have limited space on your truck. You must decide what products you will leave behind or not transport at all.

## Production:

Some several inputs and outputs need to be constantly balanced. So it can have multiple stages (like in order processing).

A good example here is the production process of ice cream treats. And also other food items like hamburgers, sandwiches, fries, etc., and their assembly lines.

## Customer Service:

How many employees should be hired? In addition to hiring and training employees, you must also keep track of their productivity and efficiency levels.

## Production Planning:

You must decide how many products you should produce using a certain quantity of resources (including people). The company has a certain number of hours per day and people per shift that can work on production processes.

## Sales/Marketing:

A good example here would be determining how many ads should be published for each product or service for maximum profit? Another example would be how many employees should work in sales for each product line?

So this can also include salary planning for each employee based on needs for selling increased sales numbers. The more sales an employee makes, the higher their salary will be.

## Budgeting:

It may seem simple at first glance but it involves a lot of variables including advertising costs, salaries, etc. In addition, it is important to determine the limits of each budget category. It is a very complex exercise.

## How To Solve Linear Programming Problems: Linear Programming Model

The linear programming model can be represented visually. It has the following components:

## Constraints

The constraints are a set of linear inequalities and equations that must be fulfilled for the problem to be optimal.

## Objective Function

This is the value of the objective function that you want to maximize or minimize. This can include costs, profits, etc. (For example, you want to maximize profit or minimize cost.)

## Variable Numbers

These are numbers that can vary in the solution – they will be used to find the optimal solutions. Because they are not fixed they are called variables in linear programming.

Some will be excluded from optimization because they are constants or fixed variables.

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