Question

Minimize S = x + 19y with xy = 19 and both x and y > 0.
and also
Minimize 8x^2+8y^2 with xy^2=16

please help! :(

Answer 1

alrigt the first problem... you have

sum=x+19y

and xy=19

Answer 2

use the second equation to solve for x or y

since x is by itself i'd solve for x

y=19/x

Answer 3

x=19/y i mean

next put this into the first equation

S=19/y+19y

Answer 4

next take S'

\[S'=-19y^{-2}+19\]

Answer 5

thank you!