Example 1
To start producing a new model of custom wheels, a company will have to purchase $30,000 in new equipment. Each wheel made costs them $40 in supplies and labor.
Write a formula for the total cost, TC, of producing q wheels. What will be their total costs in the first year if they expect to sell 240 wheels

To determine the total cost $ TC $ of producing $ q $ wheels, we need to consider both the fixed costs and the variable costs:

1. **Fixed cost**: The company needs to purchase $30,000 in new equipment. This is a one-time cost that does not change with the number of wheels produced.
2. **Variable cost**: Each wheel costs $40 in supplies and labor, so for $ q $ wheels, the variable cost is $ 40q $.

The total cost $ TC $ can be represented as:

\[
TC = 30,000 + 40q
\]

### Calculation for 240 wheels:
To find the total cost for producing 240 wheels, substitute $ q = 240 $ into the formula:

\[
TC = 30,000 + 40(240)
\]

First, calculate $ 40 \times 240 = 9,600 $.

So,

\[
TC = 30,000 + 9,600 = 39,600
\]

### Total cost for producing 240 wheels in the first year: 
\[
\boxed{39,600}
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. How would the total cost change if they produced 500 wheels?
2. What would be the average cost per wheel if they produced 240 wheels?
3. At what quantity of wheels does the total cost reach $50,000?
4. How would the formula change if the equipment cost was spread over 3 years?
5. How much would they save if labor costs were reduced by 10%?

**Tip**: Fixed costs remain the same regardless of the production volume, while variable costs increase with each unit produced.

To start producing a new model of custom wheels, a company will have to purchase $30,000 in new equipment. Each wheel made costs them $40 in supplies and labor. Write a formula for the total cost, TC, of producing q wheels. What will be their total costs in the first year if they expect to sell 240 wheels?

Learn how to calculate the total cost of producing custom wheels using a linear equation model. This problem explores fixed costs, variable costs, and offers a formula to determine the total cost for producing 240 wheels. Suitable for students in Grades 9-10.

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