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What Is a Linear Cost Function?

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  • Written By: Jim B.
  • Edited By: M. C. Hughes
  • Last Modified Date: 16 November 2014
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A linear cost function is a mathematical method used by businesses to determine the total costs associated with a specific amount of production. This method of cost estimation can be done whenever the cost for each unit produced remains the same no matter how many units are produced. When that is the case, the linear cost function can be calculated by adding the variable cost, which is the cost per unit multiplied by the units produced, to the fixed costs. Performing this equation will give the total cost for a production order, thus enabling businesses to budget accordingly and make decisions on production amounts.

Managers of businesses that focus on some kind of production or manufacturing must be aware of costs at all times. Simply counting up all of the costs after production is done can lead to major problems if the costs exceed what was expected. For that reason, managers must develop methods of cost estimation that are accurate and reliable. One simple method of cost estimation involves the use of a linear cost function.

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Using a linear cost function requires a basic understanding of how functions work. A function is a mathematical equation that is performed on any set of values that then produces a corresponding set of values. These values can be placed on a graph to study the relationship between them when the function is performed. If the function produces a straight line on the graph when the values are entered, it is known as a linear function.

For an example of how a linear cost function is utilized to estimate production costs, imagine that a company decides to fill out an order of 1,000 widgets that cost $50 US Dollars (USD) each to produce. Multiplying these two numbers produces the variable costs in this function, which turn out to be $50,000 USD. In addition to that total, it takes $3,000 USD to simply get the factory up and running for any type of production. Those costs, which are the fixed costs in this equation, are added to the variable costs to leave a total of $53,000 USD for this particular order.

It is important to note that the linear cost function in this case works because the widgets always cost the same amount to produce. If a graph was produced with the amount of widgets produced on one axis and the total costs on the other, it would reveal a straight line. This process would not work if the individual cost to make each widget varied depending on the size of the order.

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