Question

If a, b, c, d > 0 such that a + 2b + 3c + 4d = 50, then the maximum value of `((a^2b^4c^3d)/16)^(1/10)` is equal to ______.

Options

• 2.00

• 3.00

• 4.00

• 5.00

Answer 1

If a, b, c, d > 0 such that a + 2b + 3c + 4d = 50, then the maximum value of `((a^2b^4c^3d)/16)^(1/10)` is equal to 5.00.

Explanation:

`(2(a/2) + 4((2b)/4) + 3(c) + 1.(4d))/10` = 5

⇒ `5 ≥ ((a/2)^2.(b/2)^4.c^3. 4d)^(1/10)`

⇒ `((a^2b^2c^3d)/16)^(1/10) ≤ 5`