1. **State the problem:** We are given the average cost function $$AC = \frac{80}{Q} + 2 + Q$$ and we want to understand its behavior. 2. **Formula and explanation:** The average cost (AC) function is composed of three parts: a term inversely proportional to quantity $Q$, a constant term, and a term directly proportional to $Q$. 3. **Find the minimum average cost:** To find the quantity $Q$ that minimizes $AC$, we take the derivative of $AC$ with respect to $Q$ and set it to zero. $$AC = \frac{80}{Q} + 2 + Q$$ $$\frac{dAC}{dQ} = -\frac{80}{Q^2} + 1$$ Set derivative equal to zero: $$-\frac{80}{Q^2} + 1 = 0$$ 4. **Solve for $Q$:** $$1 = \frac{80}{Q^2}$$ $$Q^2 = 80$$ $$Q = \sqrt{80} = 4\sqrt{5} \approx 8.944$$ 5. **Calculate minimum average cost:** Substitute $Q = 8.944$ back into $AC$: $$AC = \frac{80}{8.944} + 2 + 8.944 \approx 8.944 + 2 + 8.944 = 19.888$$ 6. **Interpretation:** The average cost is minimized when producing approximately 8.944 units, and the minimum average cost is about 19.888. This analysis helps in understanding how production quantity affects average cost and where the cost efficiency is maximized.