Question

Solve the following question and mark the best possible option.
Find the maximum value of ab (72 – 3a  – 4b), for a, b > 0

Options

• 1112

• 1442

• 1152

• None of these

Answer 1

Let S = ab (72 – 3a – 4b)
We have AM ≥ GM

⇒ `(3a + 4b + (72 – 3a – 4b))/3 ≥ root(3)(3a xx 4b xx (72 – 3a – 4b))`

⇒ 24 ≥ (12)^1/3`root(3)( ab(72 – 3a – 4b))`

⇒ ab(72 – 3a – 4b) ≤ `(24)^3/12`

⇒ ab (72 - 3a - 4b) ≤ 1152

⇒ Maximum value of ab (72 - 3a - 4b) is 1152.