Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and the Yahoo Answers website is now in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.
Trending News
Find two nonnegative numbers whose sum is 20 and such that the product of twice one?
and the square of the other number
will be a maximum.
10 and 10, right?
1 Answer
- ?Lv 78 years agoFavorite Answer
x= one non-neg number
y= the other.
Given: x + y = 20 ....... (1)
.... 2xy^2 => Max ....... (2)
From (1): ..... y= 20 - x
(1) in (2)
z = 2x ( 20 - x )^2 => Max
z = 2x ( 400 - 40x + x^2 )
z= 800x - 80x^2 + 2x^3 => Max
Find dz/dx:
dz/dx = 800 - 160x + 6x^2 = 0 ................ Divide by 2
........... 3x^2 - 80x + 400 = 0
...........( 3x - 20)( x - 20) = 0
.............. x = 20/3 or x= 20 ................. x can not be 20 because y would be 0.
Sub x = 20/3 in (1)
...... 20/3 + y = 20
................ y = 40/3
The first number is 20/3 and the number squared is 40/ 3