KöMaL 2014 B4614

Let $x_1$,...,$x_n$ and $y_1$,...,$y_n$ be nondecreasing sequences of non-negative numbers, such that the sum of the $n$ terms is 1. $a$) What is the maximum possible value of $\min_{1\le i\le n} |x_i-y_i|$? $b$) What is the maximum possible value of $\sum_{i=1}^n{|x_i-y_i|}$?