https://file.aiquickdraw.com/mathbot/file/1725933412856agtlr16b.jpg

The question in the image asks about the number of radios that must be produced and sold in order for the company to break even. To solve a break-even problem, you generally need to find the point where the company's **cost function** and **revenue function** are equal. 

1. **Cost Function**: This includes both fixed and variable costs, often in the form \( C(x) = mx + b \), where \( m \) is the variable cost per unit, \( b \) is the fixed cost, and \( x \) is the number of radios.
   
2. **Revenue Function**: This is generally \( R(x) = px \), where \( p \) is the price at which each radio is sold, and \( x \) is the number of radios sold.

At break-even, the total cost equals the total revenue:
\[
C(x) = R(x)
\]
From the graphs (though not visible), you would locate the point of intersection between these two functions to determine the number of radios, \( x \), that the company needs to produce and sell to break even.

If you can describe the graph or provide the equations, I can help you calculate this exactly.

Would you like further details on break-even analysis or have any other questions?

### Follow-up Questions:
1. What are the specific cost and revenue functions from the graph?
2. How does fixed cost impact the break-even point?
3. What happens to the break-even point if the price per radio increases?
4. How would the company’s profit change if it sells more than the break-even number of radios?
5. How is the slope of the cost function related to variable costs?

### Tip:
Always look for the intersection of cost and revenue on a graph to find the break-even point.

The figure on the right shows the graphs of the cost and revenue functions for a company that manufactures and sells small radios. How many radios must be produced and sold for the company to break even?

Learn how to calculate the break-even point for a company that manufactures and sells small radios by analyzing cost and revenue functions. This problem involves algebraic concepts and linear functions, providing a detailed look into the break-even analysis suitable for college-level students.

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