Question

Maximize Q=xy, where x and y are positive numbers such that x+6y^2=2

Answer 1

Q = xy

x + 6y² = 2

x = 2 - 6y²

Q = (2 - 6y²) . y

Q = 2y - 6y³

Maximize, then derivate.

Q' = 2 - 18y² = 0

18y² = 2

y² = 1/9

y = ±1/3 (maximize, then positive)

x = 2 - 6y²

x = 2 - 6.1/9

x = 2 - 2/3

x = 4/3

Q = 4/3 . 1/3

Q = 4/9