Question 90
Let $a_1 \le a_2 \le \dots \le a_{50}$ be real numbers such that
(i) $a_1 + a_2 + \dots + a_{50} = 0,$
(ii) $|a_1| + |a_2| + \dots + |a_{50}| = 624.$
Find the minimum value for $S = a_{50} - a_1$ and maximum value of $T = a_1a_2 \dots a_{50}$.
(i) $a_1 + a_2 + \dots + a_{50} = 0,$
(ii) $|a_1| + |a_2| + \dots + |a_{50}| = 624.$
Find the minimum value for $S = a_{50} - a_1$ and maximum value of $T = a_1a_2 \dots a_{50}$.