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Cost function

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College Algebra

Definition

A cost function represents the cost of producing a certain number of goods or services as a function of the quantity produced. It is typically expressed in algebraic form and used to model economic behavior.

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5 Must Know Facts For Your Next Test

  1. The cost function can often be written as $C(x) = c_0 + c_1x + c_2x^2 + ... + c_nx^n$, where $c_i$ are constants and $x$ is the quantity produced.
  2. In linear cost functions, the total cost is represented by $C(x) = c_0 + c_1x$, where $c_0$ is the fixed cost and $c_1$ is the variable cost per unit.
  3. Understanding how to derive and interpret the slope and intercept in a linear cost function is crucial for analyzing production costs.
  4. Cost functions can be used to determine break-even points by setting the total revenue equal to the total cost.
  5. Cost functions are integral in solving systems of equations involving production constraints and optimization problems.

Review Questions

  • How do you represent a linear cost function algebraically?
  • What do the constants in a quadratic cost function represent?
  • Explain how you would find the break-even point using a cost function.
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