SOLUTION: Find two numbers whose sum is 16 and whose product is a maximum.

Question 1179580: Find two numbers whose sum is 16 and whose product is a maximum.
Found 2 solutions by greenestamps, josgarithmetic:
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

To get a sum of 16, let the two numbers be 8-a and 8+a, where a is constant.

The sum of the two numbers is 16; and the product is (8-a)(8+a)=64-a^2.

The maximum value of 64-a^2 is when a=0, because a^2 is always non-negative.

So the maximum value of the product is when a=0, making the two numbers 8-0=8 and 8+0=8.

ANSWER: 8 and 8

Note there is nothing special about the number 16 as the sum of the two numbers. It is always true that for a given sum of two numbers, the maximum product of the two numbers is when they are equal.

Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
x and 16-x;

Parabola with a maximum point.
Maximum y should happen at the exact middle of 0 and 16, which will be 8.

Both numbers should be 8.

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