Question
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.
add up to 120. Find the numbers which maximized the product all the three numbers.
Answers
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.
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.
eunice
why does x-z became equal to zero?