The problem asks to write a linear function for the cost of manufacturing $x$ bicycles in a day.

The linear cost function is given as $C(x) = mx + b$, where:

• $m$ represents the variable cost per bicycle,
• $b$ represents the fixed daily cost,
• $C(x)$ represents the total cost of manufacturing $x$ bicycles.

From the question, we are given:

• The fixed cost $b = 1500$ dollars per day,
• The variable cost $m = 100$ dollars per bicycle.

Thus, the cost function $C(x)$ can be written as: $C(x) = 100x + 1500$

This is the linear function that expresses the cost of manufacturing $x$ bicycles in a day.

Would you like more details on how to interpret this type of cost function?

Here are some related questions:

1. How would the cost function change if the variable cost per bicycle increased?
2. What does the slope of the cost function represent in practical terms?
3. How can this cost function help in determining the total cost for manufacturing 10 bicycles?
4. How would the fixed costs affect the graph of the cost function?
5. What happens to the total cost if no bicycles are manufactured?

Tip: Always ensure to identify fixed and variable costs when working with cost functions.