Question

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

एक टूर ऑपरेटर 50 यणस्त्रयों के स्लए रु 200 प्रस्ि यणत्री िसूल करिण है, 50 सेअस्धक मेंप्रत्येक 10

यणत्री के स्लए 5 की छू ट देिण है, उन यणस्त्रयों की संख्यण स्नधणिररि करेंजो ऑपरेटर के रणजति को

अस्धकिम करेंगे।

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Answer 1

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

Let us assume that there are x passengers

Passengers in excess of 50 = x-50

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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