Businesses need to make the most of what they have when it comes to resources like materials, labor and money. They also must choose how to spend their time and efforts to maximize the returns on their investment. These problems may seem simple, but there are often lots of variables to consider. Linear programming (LP) helps businesses optimize complex operations by depicting the various solutions in a simplified way. As a business owner, it's important that you know the advantages of linear programming as well as its drawbacks.

## Linear Programming in Action

Linear programming is widely used in management and research science as well as in business. Organizations use this method to streamline their operations in order to reduce costs and maximize profits. Their end goal is to achieve the best possible outcome. For example, a manufacturing company may use linear programming to identify ways to minimize production and inventory costs without sacrificing product quality.

Consider a bicycle manufacturer that produces mountain bikes and street bikes, each of which generates a different profit level. The manufacturer would like to know how many bikes of each category to produce so as to maximize profits, given that the business can sell its entire output.

Two different teams produce the mountain bikes and the street bikes by hand, each with production constraints in terms of how many bikes it can produce per day. The bikes also have to go through a machine finishing process that has a limited processing capacity. The business could use the linear programming technique to solve this sort of problem.

Like everything else, this method isn't perfect. Before implementing it it, make sure you have a good understanding of the advantages and disadvantages of linear programming.

## Limitation: Assumption of Linearity

The linear programming approach is based on an assumption that the world is linear. In the real world, this is not always the case. There are certain ways of mixing the inputs that a linear programming approach doesn't permit.

For instance, the bicycle manufacturer might find that if it orders materials for the two types of bicycles from the same supplier, it could cut costs. This effect can't be incorporated into a linear programming model. Linear models also don’t account for certain factors, such as an increased production efficiency as the level of production rises.

## Limitation: Fractional Values

The linear programming model assumes that inputs and outputs can be fractional. This is not always the case in the real world. For example, if a business is trying to find out how many people it should have on staff during peak business hours, this can't be a fraction.

Similarly, if a taxi business is trying to decide how many cars it should buy, this can't be a fraction either. If even one variable involved has to be in integer form, linear programming is not a suitable technique.