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The problem asks when the company starts to turn a profit, given:

- Cost function: \( C(x) = 7x + 140 \)
- Revenue function: \( R(x) = 11x \)

To determine when the company starts turning a profit, we need to find when the revenue is greater than the cost. This happens when:

\[
R(x) > C(x)
\]

Substituting the given functions:

\[
11x > 7x + 140
\]

Now, solve this inequality:

\[
11x - 7x > 140
\]

\[
4x > 140
\]

\[
x > 35
\]

So, the company will start turning a profit when the production level is at least **36** units (since it must be greater than 35).

Let me know if you'd like more details or have any questions! 

Here are five related questions:
1. How does increasing the revenue per unit affect the break-even point?
2. What if the fixed cost (currently 140) increases—how does that impact profit?
3. Can you determine the break-even point by equating the cost and revenue functions?
4. How would the profit function \( P(x) = R(x) - C(x) \) look in this case?
5. What happens to the profit if the variable cost per unit changes?

**Tip:** Always check for break-even by setting revenue equal to cost, then find the point when revenue exceeds cost for profitability!

A fast-food restaurant has a cost of production C(x) = 7x + 140 and a revenue function R(x) = 11x. When does the company start to turn a profit?

Learn how to determine when a company starts turning a profit by solving a linear inequality between cost and revenue functions. This problem involves algebraic concepts like linear equations and inequalities, suitable for high school students.

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