Question

Minimize S = x + 19y with xy = 19 and both x and y > 0.

Answer 1

S = 19/y + 19y

Answer 2

differentiate S w.r.t y and set it equal to 0

Answer 3

S' = -19/y^2 + 19 = 0

Answer 4

y^2 = 1

Answer 5

y = 1 or -1

Answer 6

y can't be negative, so y = 1

Answer 7

x = 19