SOLUTION: Find two positive real numbers whose sum is 40 and whose product is a maxium. Construct the function f(x) = x(40 - x). How is this found?

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Question 3420: Find two positive real numbers whose sum is 40 and whose product is a maxium.
Construct the function f(x) = x(40 - x).
How is this found?
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
Let the 2 numbers be x and y.

so, we are told that x+y=40 --eqn1
and that xy is to be a maximum.

so we have the function f(x) = xy. Now get rid of y by using eqn1 (written as y = 40-x... so f(x) = x(40-x)...easy enough?

We are told to find those 2 numbers that have the largest product (ie 1x39, 2x38, 3x37 etc)...

dy/dx = 40 - 2x = 0
so, x=20
so therefore, y must be 20 too

this is the answer: x=y=20

jon