Question

Find two positive numbers x and y such that x + y = 60 and xy³ is maximum.

Answer 1

Let P = xy³

It is given that x + y = 60

⇒ x = 60 − y

For maximum or minimum values of y, P we have

P is maximum when y = 45

when y = 45

x + y = 60

⇒ x = 60 − 45

x = 15

Numbers are 15 and 45.