Let $y_1,\ldots y_n$ be positive real numbers satisfying
$y_1+\cdots+y_n\geq n$ and $\displaystyle{\frac{1}{y_1}+\cdots+\frac{1}{y_n}\geq n}$.
Is it true that $y_1y_2\cdots y_n\geq 1$?
Let $y_1,\ldots y_n$ be positive real numbers satisfying
$y_1+\cdots+y_n\geq n$ and $\displaystyle{\frac{1}{y_1}+\cdots+\frac{1}{y_n}\geq n}$.
Is it true that $y_1y_2\cdots y_n\geq 1$?