Question

a tour operator charge rs 200 per passenger for 50 passenger with a discount of rs 5 for each 10 passenger in excess of 50 determine the number of passengers that will maximize the revenue of the operator​

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Answer 1

hence the answer is 500 passengers

Answer 2

The number of passengers that will maximize the revenue of the operator is 225

Step-by-step explanation:

Given:

A tour operator charges Rs. 200 per passenger for 50 passengers

To find out:

The number of passengers that will maximize the revenue

Solution:

For 50 passengers, the tour operator will get

$=50\times 200$ Rs.

$=10000$ Rs.

Let us assume that x passengers

Passengers in excess of 50 = 50 - x

For every 10 passengers in excess of 50 he charges 5 Rs. less

Thus

$R=(x)[200-\frac{5}{10}(x-50)]$    where $x\ge 50$

Thus, the revenue

$R=200x-\frac{1}{2}(x^2-50x)$

For Max R

$\frac{dR}{dx}=0$

$\implies 200-\frac{1}{2}\times (2x-50)=0$

$\implies 200-x+25=0$

$\implies x=225$

Now,

$\frac{d^2R}{dx^2}=-1<0$

Hence at $x=225$ Revenue R is maximum

Therefore, number of passengers that will maximize the revenue of the operator is 225

Hope this answer is helpful.

Know More:

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