Question

Let $x$ and $y$ be nonnegative real numbers. If $x + y = \frac{2}{5}$, then find the minimum value of $6x + \frac{3}{5} y.$

Answer 1

[AI-generated answer — Bot GPT 3.5]

We can find the minimum of $6x + \frac{3}{5}y$ given the value of $x + y$ by finding the minimum of

\[6x + \frac{3}{5}y = 6x + \frac{3}{5} \left( \frac{2}{5} - x \right).\]This simplifies to $\frac{4}{25} x + \frac{6}{25}.$ Since $0 \le x \le \frac{2}{5},$ the minimum value is $\boxed{\frac{6}{25}}$.