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Minimize S = x + 18y with xy = 18 and both x and y > 0?
I need help solving for S.
1 Answer
- ?Lv 69 years agoFavorite Answer
first use x = 18/y
plug into original equation for S
S = 18/y + 18y
now take the derivative
dS/dy = -18/y^2 + 18
so we will have a critical point at -18/y^2 + 18 = 0
18/y^2 = 18
y^2 = 1
y = 1
plugging y = 1 into xy = 18 gives
x = 18
So the minimum value for S is
x + 18y
18 + 18(1)
=36
If you use x = 9 and y = 2 you get 9 + 2*18 which is higher then 36. Likewise, if you use x = 36 and y = .5 you get 36 + .5*18 which is also higher than 36. So we have found the minimum.
Hope this helps.