Question 873702: Help find two numbers whose sum is 700 and whose product is a maximum. Found 2 solutions by KMST, Fombitz:Answer by KMST(5328) (Show Source):
You can put this solution on YOUR website! = one of the numbers. = the other number. = the product of those two numbers.
That is a quadratic function, and is usually written as .
The graph is a parabola, looking like this: .
Where is its maximum?
You may have been shown, and it can be proven that the maximum of a quadratic like is at
So in this case the maximum happens when .
Of course, that means that the other number is .
That is not surprising because it is the same as asking you what rectangle with a half-perimeter of 700 has the greatest area, and we know it is a square.
The same problem could also be asked as what is the largest rectangular plot that can be fenced when you have 1400 feet of fencing.
