Let S =x1y1+ x2y2 +……..+ xnyn,Where x1,x2………. x nand y1,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 lakes its minimum value over all orderings of the two sequences when one sequence is sorted into nondecreasing order and the other is sorted into nonincreasing order.
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