give me a 5/10 medium complex graphing question that applies in the real world

Here's a medium-complexity graphing question that applies to the real world:

**Question:**

A company produces and sells smartphones. The company's total cost (including fixed and variable costs) to produce $x$ smartphones can be modeled by the equation:

\[
C(x) = 5000 + 150x
\]

Where:
- $C(x)$ is the total cost in dollars,
- $x$ is the number of smartphones produced.

The company sells each smartphone for $300, so the revenue function is given by:

\[
R(x) = 300x
\]

1. Graph the cost function $C(x)$ and the revenue function $R(x)$ on the same coordinate plane for $x$ values between 0 and 100.

2. Determine the break-even point, where the company's revenue equals its costs.

3. Shade the region where the company is making a profit.

4. What is the minimum number of smartphones the company must produce to make a profit?

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Would you like any details or further clarifications on this question? 

Here are 5 related questions you could explore:

1. How would the graph change if the fixed cost increased to $7000?
2. What if the company decides to sell smartphones at $250 each, how does that affect the break-even point?
3. How would the profit region shift if the variable cost per smartphone increased to $200?
4. If the company wants to earn a profit of $20,000, how many smartphones must it sell?
5. What is the significance of the slope of the revenue and cost functions in this scenario?

**Tip:** In real-world graphing problems, always pay attention to the intersections of cost and revenue to identify break-even points and profit regions.

Explore a real-world graphing problem involving cost and revenue functions for a company that produces smartphones. Learn how to graph the functions, find the break-even point, and calculate the profit region. Suitable for high school students in Grades 10-12.

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