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.

To calculate the number of parts needed to cover the cost of the injury, we first need to determine the profit made per part.

### Step 1: Calculate the profit per part
Given:
- The cost of each component is $14.75.
- The profit margin is 12%.

Profit per part is calculated as:
\[
\text{Profit per part} = 12\% \times 14.75
\]
\[
\text{Profit per part} = 0.12 \times 14.75 = 1.77
\]

### Step 2: Calculate the number of parts needed to cover the cost
The total cost of the injury is $7,200. To find the number of parts required to cover this cost, divide the total cost by the profit per part:
\[
\text{Number of parts} = \frac{\text{Total cost of injury}}{\text{Profit per part}}
\]
\[
\text{Number of parts} = \frac{7200}{1.77} \approx 4067.8
\]

Since the number of parts must be a whole number, round up to the next whole number:
\[
\text{Number of parts} = 4068
\]

### Final Answer:
The facility needs to produce and sell **4,068 parts** to cover the $7,200 injury cost.

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Would you like more details or have any questions? 

Here are some related questions you might consider:
1. How would the required number of parts change if the profit margin increased to 15%?
2. What if the cost of each component increased to $16.50, keeping the same profit margin?
3. How would the total revenue change if they produce 5,000 parts?
4. How much total profit would be made from selling 4,068 parts?
5. What are the potential consequences of such an injury cost on the overall profitability?

**Tip:** When dealing with financial problems, always ensure to account for rounding and ensure the calculations are practical in real-world scenarios.

Learn how to calculate the number of parts needed to cover a $7,200 injury cost in manufacturing. This problem involves determining profit per part and using division to find the total parts required. Suitable for anyone needing to understand cost coverage in production scenarios.

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