The RideEm Bicycles factory can produce 110 bicycles in a day at a total cost of $10,200. It can produce 130 bicycles in a day at a total cost of $10,900. What are the company's daily fixed costs (in dollars)?
$ 
 
What is the marginal cost (in dollars) per bicycle?

To find the daily fixed costs and the marginal cost per bicycle, we can model the total cost as a linear function of the number of bicycles produced. This means the total cost $ C(x) $ can be expressed as:

\[
C(x) = mx + b
\]

where:
- $ C(x) $ is the total cost,
- $ x $ is the number of bicycles produced,
- $ m $ is the marginal cost per bicycle,
- $ b $ is the fixed cost (which remains constant regardless of how many bicycles are produced).

### Step 1: Set up two equations based on the information provided.
For 110 bicycles, the total cost is $10,200:
\[
10,200 = 110m + b
\]
For 130 bicycles, the total cost is $10,900:
\[
10,900 = 130m + b
\]

### Step 2: Solve the system of equations.
Subtract the first equation from the second to eliminate $ b $:

\[
(10,900 - 10,200) = (130m - 110m)
\]
\[
700 = 20m
\]

Solve for $ m $ (the marginal cost per bicycle):
\[
m = \frac{700}{20} = 35
\]

So, the marginal cost per bicycle is **$35**.

### Step 3: Find the fixed cost.
Substitute $ m = 35 $ into one of the original equations, say $ 10,200 = 110m + b $:

\[
10,200 = 110(35) + b
\]
\[
10,200 = 3,850 + b
\]
\[
b = 10,200 - 3,850 = 6,350
\]

So, the fixed cost is **$6,350**.

### Final answers:
- **Fixed cost:** $6,350
- **Marginal cost per bicycle:** $35

Would you like further details or have any questions?

Here are 5 related questions you might find interesting:
1. How does increasing the marginal cost affect overall production costs?
2. If the factory produces 150 bicycles, what would be the total cost?
3. What would be the breakeven point if each bicycle is sold for $100?
4. How does a change in fixed costs impact the marginal cost?
5. What if the cost of materials increases, how might that impact the marginal cost?

**Tip:** Marginal cost is useful for understanding how much extra it costs to produce each additional unit in manufacturing.

The RideEm Bicycles factory can produce 110 bicycles in a day at a total cost of $10,200. It can produce 130 bicycles in a day at a total cost of $10,900. What are the company's daily fixed costs (in dollars)? What is the marginal cost (in dollars) per bicycle?

Learn how to determine the fixed costs and marginal cost per bicycle for a factory that produces 110 bicycles at a cost of $10,200 and 130 bicycles at a cost of $10,900. This problem uses linear cost functions to find solutions and is suitable for students in Grades 9-12.

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