A tour operator charges ₹136 per passenger for 100 passengers with a…

The correct answer is Option (3) → 220

Let the number of passengers that are in excess of 100 be 10x, then amount received by the tour operator is

$A = (100+ 10x) (136 - 4x)$

$⇒A = 13600-400x + 1360x-40x^2$

$⇒A = 13600 + 960x - 40x^2$

Diff. w.r.t. x, we get

$\frac{dA}{dx}=0+960-80x$

and $\frac{d^2A}{dx^2}= -80$.

Now, $\frac{dA}{dx}=0⇒960-80x = 0⇒x= 12$.

Also, $\left[\frac{d^2A}{dx^2}\right]_{x=12}=-80<0$

⇒ A is maximum at $x = 12$.

Hence, the number of passengers for which the tour operator received maximum amount is $100 + 10 × 12$ i.e. 220.