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The problem in your image asks you to create a linear cost function for manufacturing bicycles, using the form $ C(x) = mx + b $, where:

- $ b $ is the fixed cost,
- $ m $ is the variable cost per unit (cost per bicycle in this case),
- $ x $ is the number of bicycles manufactured.

### Given information:
- The fixed cost ( $ b $ ) is $1500 per day.
- The variable cost ( $ m $ ) is $80 per bicycle.

### Solution:
The linear cost function can be written as:

\[
C(x) = 80x + 1500
\]

Where:
- $ 80x $ represents the total variable cost (number of bicycles times the cost per bicycle),
- 1500 is the fixed cost.

So, the linear function that expresses the cost of manufacturing $ x $ bicycles in a day is:

\[
C(x) = 80x + 1500
\]

Would you like further details on how this function works or how to interpret slope-intercept form?

### Follow-up Questions:
1. How would the cost function change if the fixed cost increased?
2. What happens to the total cost if no bicycles are produced?
3. How does the variable cost affect the total cost as the number of bicycles increases?
4. How would the cost function change if each bicycle cost $100 instead of $80?
5. Can you graph this cost function and explain its components?

### Tip:
The slope in the cost function represents how the total cost changes with each additional unit produced, making it a critical factor in understanding manufacturing expenses.

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 $1500 and each bicycle costs $80 to manufacture. (a) Write a linear function that expresses the cost of manufacturing x bicycles in a day.

Solve a linear cost function problem where a bicycle manufacturer has fixed daily costs of $1500 and variable costs of $80 per bicycle. Learn how to express this relationship in slope-intercept form, suitable for students in Grades 9-12.

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