1. **State the problem:** We have a cost function $$C(x) = 0.2x^2 - 10x + 200$$ where $x$ is the number of drinks sold. We want to find: (a) The number of drinks $x$ that minimizes the cost. (b) The minimum cost value. 2. **Formula and rules:** For a quadratic function $$C(x) = ax^2 + bx + c$$ with $a > 0$, the minimum occurs at $$x = -\frac{b}{2a}$$. 3. **Find the number of drinks to minimize cost:** Given $$a = 0.2$$ and $$b = -10$$, $$x = -\frac{-10}{2 \times 0.2} = \frac{10}{0.4}$$ $$x = 25$$ 4. **Calculate the minimum cost:** Substitute $x=25$ into the cost function: $$C(25) = 0.2(25)^2 - 10(25) + 200$$ $$= 0.2 \times 625 - 250 + 200$$ $$= 125 - 250 + 200$$ $$= 75$$ **Final answers:** (a) The number of drinks to minimize cost is $25$. (b) The minimum cost is $75$.