# Business uses of a linear programming model

Written by sue smith
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Linear programming offers mathematical techniques with which businesses and other organisations can develop methods to produce optimum outcomes. With linear programming, a variety of quantities and constraints are balanced with desired outcomes, helping business managers to make decisions that best serve these outcomes. Linear programming is used to carry out optimisation in a variety of business environments, including financial, manufacturing, personnel and logistics management.

## Factors

Linear programming models formalise various factors of an activity to be optimised in terms of constraints, quantities, data and linear relationships. With a linear model, a business manager can define the variables they wish to optimise, the factors for which a decision may be made, constraints on such decisions and the data values to feed into the process. Essentially, linear programming can help business managers to take decisions based on what their priorities are, taking into account the various factors affecting the activity in question, for example a manufacturing process or people management decision.

## Maximising profit

A typical use for linear programming in business is maximising profit. With linear programming, business managers can define the variables within some business process such as manufacturing a product, building in constraints as necessary and calculating which choices optimise on profits within these parameters. The outcome of using linear programming for such a purpose may involve one or more decisions within the business. When it comes to economic decisions, linear programming models can be particularly useful in cases where the variables and constraints are sufficiently complex to benefit from computer processing.

## Minimising cost

Similar to maximising profit, linear programming can be used by business managers looking to minimise on costs. Typical examples of this could be for industrial processes or even personnel management decisions. By feeding the variables and constraints in the decision into a linear programming modelled system, managers can use a concrete calculation to arrive at the choice, or choices, which will best serve the optimisation of cost. Often the decisions calculated to optimise on profits and costs will be related.

## Decisions

While linear programming models can be used to make informed decisions about future planning, they must be seen within a business context that may be complex. For example, while a linear programming approach to a particular decision may help the business manager to take the right decision for one particular priority, such as cost, there may be other issues within the business as a whole affecting the outcome. This means that a linear programming approach to taking particular decisions can only be effective if the data used is accurate, exhaustive and relevant. By its nature, linear programming can only inform planning decisions that can be formalised using numeric values, such as financial planning.

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