Let S = xlYI + X2 Y2 + ... + XnYn, where XI , X2 , ... ,

Chapter 1, Problem 1.7.35

(choose chapter or problem)

Let S = xlYI + X2 Y2 + ... + XnYn, where XI , X2 , ... , Xn and YI , Y2 , .. , Yn are orderings of two different sequences of positive real numbers, each containing n elements. a) Show that S takes its maximum value over all orderings of the two sequences when both sequences are sorted (so that the elements in each sequence are in nondecreasing order). b) Show that S takes its minimum value over all orderings ofthe two sequences when one sequence is sorted into nondecreasing order and the other is sorted into nonincreasing order.