Of all possible pairs of positive numbers having a sum of 72, which pair has the maximum product?
A) 27 and 45
B) 26 and 46
C) 36 and 36
D) 35 and 37

Question

Quizplus · Accepted Answer

The maximum product of two numbers with a fixed sum is achieved when the two numbers are equal. This is because of the arithmetic mean-geometric mean inequality, which states that for any non-negative numbers a and b, the square of the arithmetic mean (AM) is always greater than or equal to the geometric mean (GM), with equality only when a = b. Here, since the sum is 72, dividing it equally gives us 36 and 36, which maximizes the product.

Of All Possible Pairs of Positive Numbers Having a Sum