A manufacturing facility produces automotive components and expects a profit of 12% on each part produced. They have a more serious injury that results in a direct cost of $7,200. The cost of each component sold is $14.75. Calculate the number of parts that are needed to cover this cost of loss. Show your work.


To determine the number of parts needed to cover the cost of the injury, we can follow these steps:

### Step 1: Identify the given data
- **Direct Cost of Injury**: $7,200
- **Profit Margin**: 12% (or 0.12)
- **Selling Price per Component**: $14.75

### Step 2: Calculate the profit per component
The profit made on each component can be calculated using the profit margin:

\[
\text{Profit per Component} = \text{Selling Price per Component} \times \text{Profit Margin}
\]

\[
\text{Profit per Component} = 14.75 \times 0.12 = 1.77
\]

So, the profit from each component is $1.77.

### Step 3: Calculate the number of parts needed to cover the cost of the injury
Now, we need to determine how many components need to be sold to cover the $7,200 cost:

\[
\text{Number of Components} = \frac{\text{Direct Cost of Injury}}{\text{Profit per Component}}
\]

\[
\text{Number of Components} = \frac{7,200}{1.77} \approx 4,068.36
\]

Since you can't sell a fraction of a component, you would need to sell **4,069 components** to cover the cost of the injury.

### Interpretation
The company must sell approximately 4,069 components to offset the $7,200 cost from the injury. This demonstrates the significant impact even a single injury can have on the business, requiring a large volume of sales to break even.

### Do you have any questions or would you like more details?

Here are 5 related questions to consider:
1. How would the required number of components change if the profit margin were increased to 15%?
2. What would be the financial impact if similar injuries occurred multiple times within a year?
3. How can the company reduce the financial burden of workplace injuries?
4. How does the cost of the component (e.g., materials and labor) affect the overall profit margin?
5. What are the potential indirect costs associated with serious injuries in the manufacturing facility?

**Tip:** Regularly review and improve safety protocols to minimize workplace injuries, as they can lead to significant financial losses requiring substantial sales to recover.

Learn how to calculate the number of automotive components required to cover a $7,200 injury cost in a manufacturing facility. This problem involves understanding profit margins, cost analysis, and determining break-even points. Suitable for advanced high school students or professionals in manufacturing economics.

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