The RideEm Bicycles factory can produce 150 bicycles in a day at a total cost of $10,800, and it can produce 170 bicycles in a day at a total cost of $11,600.


Let's define the variables involved and solve for the cost structure.

1. Let the total cost $ C $ be a linear function of the number of bicycles $ x $ produced:
   \[
   C(x) = mx + b
   \]
   where $ m $ is the marginal cost (cost per additional bicycle) and $ b $ is the fixed cost (the cost when no bicycles are produced).

2. We are given two points of dataLet's define the variables involved and solve for the cost structure.

1. Let the total cost $ C $ be a linear function of the number of bicycles $ x $ produced:
   \[
   C(x) = mx + b
   \]
   where $ m $ is the marginal cost (cost per additional bicycle) and $ b $ is the fixed cost (the cost when no bicycles are produced).

2. We are given two points of 
   - When 150 bicycles are produced, the total cost is $10,800: 
     \[
     10,800 = 150m + b
     \]
   - When 170 bicycles are produced, the total cost is $11,600:
     \[
     11,600 = 170m + b
     \]

### Step 1: Solve the system of equations
We now have a system of two linear equations:
\[
\begin{aligned}
10,800 &= 150m + b \\
11,600 &= 170m + b
\end{aligned}
\]
We can solve this system to find $ m $ and $ b $.

Let me solve this for you.The solution to the system of equations is:

- $ m = 40 $, which means the marginal cost per additional bicycle is $40.
- $ b = 4800 $, which means the fixed cost (when no bicycles are produced) is $4800.

Thus, the cost function $ C(x) $ can be written as:
\[
C(x) = 40x + 4800
\]

This means the total cost is $4800 regardless of production, and each additional bicycle adds $40 to the total cost.

Would you like more details on this, or do you have any questions?

Here are 5 related questions:
1. What would be the total cost to produce 200 bicycles?
2. How many bicycles can be produced if the total cost is $15,000?
3. What is the average cost per bicycle at 150 bicycles?
4. How does the fixed cost affect the cost structure in the long run?
5. Can this cost model be applied to other products with similar production dynamics?

**Tip:** When dealing with cost functions, fixed costs do not change with production levels, but marginal costs increase with each additional unit.

The RideEm Bicycles factory can produce 150 bicycles in a day at a total cost of $10,800, and it can produce 170 bicycles in a day at a total cost of $11,600.

Learn how to calculate the cost structure for RideEm Bicycles, where the factory produces 150 bicycles at a cost of $10,800 and 170 bicycles at a cost of $11,600. Solve the linear equation to determine the marginal cost and fixed costs. Suitable for students in Grades 9-12.

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