x, y > 0 and x³y² = 2¹⁵

Now, 3x + 2y = (x + x + x) + (y + y)

So, by A.M $$\ge$$ G.M inequality

$${{3x + 2y} \over 5} \ge \root 5 \of {{x^3}\,.\,{y^2}} $$

$$\therefore$$ $$3x + 2y \ge 5\root 5 \of {{2^{15}}} \ge 40$$

$$\therefore$$ Least value of $$3x + 4y = 40$$