Question

Find three positive numbers whose sum is 100 and whose product is a maximum.

Answer 1

@amistre64 How do I do this without the use of Lagrange Multipliers?

Answer 2

hhmmm
i must admit i don't know what lagrange multipliers are

but intuition tells me they are 32, 33 and 34

Answer 3

assuming we are talking whole numbers

Answer 4

When they dont have to be whole numbers they are 100/3 = 33.333

But I don't know how to do them with
fx = 0 fy = 0
-that method

Answer 5

how about this:
x+y+z = 100 ---> z = 100-x-y
f(x,y,z) = x y z

f(x,y)= x y (100 - x -y) = 100xy -x^2 y - xy^2
fx= 100y -2 xy - y^2
fy = 100x - x^2 - 2 x y

set fx =0 and fy =0
solve for x (or y)

Answer 6

Ah thanks!

I didn't think of getting z and plugging that into the xyz equation!

Thanks!!