Find two positive real numbers whose product is a maximum. (Enter your answers as a comma-separated list.) The sum of the first and three times the second is 54.

Answer 1

x+3y=54

max xy

(54-3y)(y)=54y-3y^2

take the derivarive

54-6y=0

y=9

x=54-3(9)=27

xy=243 is max xy

27, 9