1. **State the problem:** We have revenue function $R(x) = 110x$ and cost function $C(x) = 60x + 7500$, where $x$ is the quantity sold. 2. **Find when profit is positive:** Profit $P(x) = R(x) - C(x) = 110x - (60x + 7500) = 110x - 60x - 7500 = 50x - 7500$. 3. **Set profit greater than zero:** $$50x - 7500 > 0$$ 4. **Solve inequality:** $$50x > 7500$$ $$\cancel{50}x > \cancel{7500}$$ $$x > 150$$ 5. **Interpretation:** The company makes a positive profit when it sells more than 150 units. 6. **Find profit when selling at price 100 per unit:** Given price per unit is 100, revenue is $R(x) = 100x$. Profit is: $$P(x) = R(x) - C(x) = 100x - (60x + 7500) = 40x - 7500$$ 7. **Find $x$ when profit is zero:** $$40x - 7500 = 0$$ $$40x = 7500$$ $$\cancel{40}x = \cancel{7500}$$ $$x = 187.5$$ 8. **Interpretation:** At price 100 per unit, the company breaks even at 187.5 units sold. 9. **Find $x$ when total revenue is 1250:** Given $R(x) = 110x$, set: $$110x = 1250$$ $$\cancel{110}x = \cancel{1250}$$ $$x = \frac{1250}{110} = 11.36$$ 10. **Interpretation:** The company sells approximately 11.36 units to have total revenue 1250. **Final answers:** - Profit positive when $x > 150$ - Break-even at $x = 187.5$ units if price is 100 - Revenue 1250 at $x \approx 11.36$ units