Math Problem Statement

Your college newspaper, The Collegiate Investigator, has fixed production costs of $74 per edition and marginal printing and distribution costs of 39¢ per copy. The Collegiate Investigator sells for 49¢ per copy. (a) Write down the associated cost function C(x) in dollars.

Solution

To write the cost function C(x)C(x), where xx is the number of copies of the newspaper produced and sold, we need to account for two parts:

  1. Fixed costs: These are costs that do not change with the number of copies produced. In this case, the fixed production costs are $74 per edition.

  2. Variable costs: These are costs that vary with the number of copies. The marginal printing and distribution costs are given as 39¢ per copy, which is $0.39 per copy.

Thus, the total cost function C(x)C(x) can be expressed as: C(x)=74+0.39xC(x) = 74 + 0.39x Where:

  • 7474 is the fixed cost in dollars,
  • 0.39x0.39x represents the variable cost for xx copies.

This cost function accounts for both fixed production costs and variable costs depending on the number of copies printed.

Let me know if you'd like further details or clarification! Here's a list of related questions:

  1. What would the cost function look like if the fixed production costs were higher?
  2. How do the fixed and variable costs affect the price point for the newspaper?
  3. If the number of copies sold increases, how does that affect total costs?
  4. What would be the total cost if 500 copies were printed?
  5. How can you calculate profit from the cost and revenue functions?

Tip: The total cost function helps in understanding how the overall production costs are influenced by the number of units produced.

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Math Problem Analysis

Mathematical Concepts

Linear Functions
Cost Functions

Formulas

C(x) = 74 + 0.39x

Theorems

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Suitable Grade Level

Grades 9-12