Cost Function  The simplest cost function is the linear cost function Upper C left parenthesis x right parenthesis equals mx plus b comma where the​ y-intercept b represents the fixed cost of operating a business and the slope m represents the variable costs.  Suppose that a small bicycle manufacturer has daily fixed costs of  ​$1800 and each bicycle costs ​$80 to manufacture.
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Part 1
​(a)  Write a linear function that expresses the cost of manufacturing x bicycles in a day.
​C(x)equals

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Given the fixed cost $ b = 1800 $ dollars and the variable cost per bicycle $ m = 80 $ dollars, the cost function can be written as:

\[
C(x) = 80x + 1800
\]

Here, $ C(x) $ represents the total cost of manufacturing $ x $ bicycles in a day.

Would you like more details or have any questions about this?

Here are 5 related questions that expand on this topic:

1. How would the cost function change if the variable cost per bicycle increased to $100?
2. What does the slope of the cost function indicate in terms of production costs?
3. How would you find the total cost for manufacturing 50 bicycles in one day using this cost function?
4. How can you determine the number of bicycles that need to be manufactured for the total cost to reach $5000?
5. How does the cost function change if the fixed cost increases by $500?

**Tip:** Understanding the components of a cost function helps in budgeting and pricing decisions in a business.

The simplest cost function is the linear cost function C(x) = mx + b, where the y-intercept b represents the fixed cost of operating a business and the slope m represents the variable costs. Suppose that a small bicycle manufacturer has daily fixed costs of $1800 and each bicycle costs $80 to manufacture. Write a linear function that expresses the cost of manufacturing x bicycles in a day.

Understand how to calculate the total cost of manufacturing bicycles using a linear cost function. This problem involves a fixed cost of $1800 and a variable cost of $80 per bicycle. Learn how to express the total cost of manufacturing x bicycles in a day. Suitable for high school students in Grades 9-12.

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