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The problem is asking how many radios must be produced and sold for the company to break even, based on the graph of cost and revenue functions provided.

### Information from the image:
- **Cost function:** \( C(x) = 6,750 + 29x \) (where \( x \) is the number of radios produced)
- **Revenue function:** \( R(x) = 89x \)

To find the break-even point, we need to determine when **cost** equals **revenue**, i.e., \( C(x) = R(x) \).

### Set the equations equal to each other:
\[
6,750 + 29x = 89x
\]

### Solve for \( x \):

1. Subtract \( 29x \) from both sides:
   \[
   6,750 = 89x - 29x
   \]

2. Simplify:
   \[
   6,750 = 60x
   \]

3. Divide by 60:
   \[
   x = \frac{6,750}{60} = 112.5
   \]

Since \( x \) represents the number of radios, it must be a whole number. Therefore, the company needs to produce and sell **113 radios** to break even.

Would you like further details or have any questions?

### Related Questions:
1. How would the break-even point change if the cost per radio increases?
2. What happens if the fixed cost increases to 7,500 instead of 6,750?
3. How is the slope of the revenue function related to the price per radio?
4. What is the marginal cost in this scenario, and how does it affect profitability?
5. How would reducing the variable cost per radio affect the break-even point?

#### Tip:
Always check that both cost and revenue functions are based on the same variable units (like per radio) to avoid confusion in financial modeling.

How many radios must be produced and sold for the company to break even, based on the graph of cost and revenue functions provided?

Learn how to calculate the break-even point for a company producing and selling radios using cost and revenue functions. This problem involves solving linear equations to determine when cost equals revenue. Suitable for students in Grades 9-12.

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