Asked by eunice

The sum of three positive numbers is 60. The first plus twice the second plus three times the third
add up to 120. Find the numbers which maximized the product all the three numbers.
Answered by oobleck
x+y+z = 60
x+2y+3z = 120

x-z = 0
so x=z
and we have
f(x) = x^2(60-2x)
f'(x) = 120x - 6x^2 = 6x(20-x)
so the numbers are 20,20,20

as usual, maximum volume of a prism (for a given surface area) is when it is a cube.
Answered by eunice
why does x-z became equal to zero?
There are no AI answers yet. The ability to request AI answers is coming soon!