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!