Question

If 3a+2b+2c=14 find the maximum value of a^3b^2c^2

Answer 1

AM >= GM

(3a+2b+2c)/7 >= (a^3b^2c^2)^(1/7)

14/7 >= (a^3b^2c^2)^(1/7)

(a^3b^2c^2)^(1/7) <= 2

a^3b^2c^2 <= 2^7

a^3b^2c^2 <= 128


Hence maximum value of a^3b^2c^2 is 128.