How do you find two numbers whose difference is 100 and whose product is a maximum?

1 Answer
Wataru
Sep 26, 2014

Unfortunately, there is no solution for this question since the product can be made as big as you wish. For any x and y that satisfy the condition, (x+1) and (y+1) will yield a larger product assuming that x and y are nonnegative.

(x+1)(y+1)=xy+x+y+1>xy

I have a feeling that the question might have been either "whose sum is 100" or "whose product is minimum ."

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