Among all pairs of numbers with a sum

Answered question

2022-05-02

Among all pairs of numbers with a sum of 83, find the pair whose product is maximum. Write your answers as fractions reduced to lowest terms.

Answer & Explanation

karton

karton

Expert2022-07-07Added 613 answers

x + y = 83
Product = xy = x(83-x) = 83x-x^2


P(x) = -x^2+83x
Max occurs when x = -b/2a = -83/(-2) = 83
If x = 83/2, y = 83/2

maximum product=83/2 *83/2=6889/4

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