Suppose two positive integers satisfy the conditions that the sum of the first number and twice the second is 120 and their product is a maximum. Then the two numbers are

A)25,70
B)27,66
C)28,64
D)29,62
E)30,60

Question

Suppose two positive integers satisfy the conditions that the sum of the first number and twice the second is 120 and their product is a maximum. Then the two numbers are
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A)25,70
B)27,66
C)28,64
D)29,62
E)30,60

Quizplus · Accepted Answer

To maximize the product of two numbers given a sum, the numbers should be as close to each other as possible due to the arithmetic mean-geometric mean inequality. Given the equation x + 2y = 120, rearranging for y gives y = (120 - x)/2. To get the numbers close to each other, x should be close to 2y, suggesting x and y should be around 40, making option E) 30,60 the closest to this ideal distribution.

Suppose Two Positive Integers Satisfy the Conditions That the Sum