Two numbers have a sum of 72. What is their product if it is a maximum?

Question

anonymous · Answer

Well, I think you mean their sum in the second part of the question, and that would just be 72 again.

dumbcow · Answer

i believe its always a max when numbers are same
36+36 = 72
max product = 36^2

dumbcow · Answer

heres the reason:

x +y = 72     ----> y = 72-x
P = xy

P = x(72-x) = 72x - x^2

take derivative and set equal to 0
---> 72 - 2x = 0
x = 36

anonymous · Answer

half of 72 should do it

anonymous · Answer

i doubt it is a calculus problem, although i could be wrong

perl · Answer

36^2

aum · Answer

Let one number be x.
The other number will be (72 - x).
Their product y = x * (72 - x) = 72x - x^2 
y = -x^2 + 72x
This is a parabola that opens downward.
Therefore, it attains its maximum at the vertex.
The x-coordinate of the vertex of a parabola is given by -b/2a 
which here is -72/(2*(-1)) = 36.

So the product is maximum when x = 36 which makes the other number 72-36=36.