1. **State the problem:** We are given the profit function $$P(x) = 850x - 0.1x^2 - 4000$$ where $x$ is the number of units produced and sold. We need to find: a. The profit when 100 units are produced, i.e., $P(100)$. b. The profit when 8400 units are produced, i.e., $P(8400)$. 2. **Recall the formula:** The profit function is quadratic: $$P(x) = 850x - 0.1x^2 - 4000$$ 3. **Calculate $P(100)$:** $$P(100) = 850(100) - 0.1(100)^2 - 4000$$ $$= 85000 - 0.1(10000) - 4000$$ $$= 85000 - 1000 - 4000$$ $$= 85000 - 5000$$ $$= 80000$$ Interpretation: When 100 units are produced and sold, the profit is 80000. 4. **Calculate $P(8400)$:** $$P(8400) = 850(8400) - 0.1(8400)^2 - 4000$$ First calculate each term: $$850 \times 8400 = 7140000$$ $$8400^2 = 70560000$$ $$0.1 \times 70560000 = 7056000$$ Now substitute: $$P(8400) = 7140000 - 7056000 - 4000$$ $$= (7140000 - 7056000) - 4000$$ $$= 84000 - 4000$$ $$= 80000$$ So, the profit from producing and selling 8400 units is also 80000. **Final answers:** - $P(100) = 80000$ - $P(8400) = 80000$