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.with explaination
Answers
Given : 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.
To find : The number of passengers that will maximize the revenue of the operator.
Solution:
- Now we have given that operator charge Rs 200 per passenger for 50 passenger, so revenue will be:
= 200 x 50
= Rs 10000
- Now discount of Rs 5 for each 10 passenger in excess of 50 will be:
- Consider 10x Passenger in excess of 50.
- So the charges will be: 200 - 5x
- Now revenue is:
= (200 - 5x)(50 + 10x)
= 10000 + 2000x - 250x - 50x²
= 10000 + 1750x - 50x²
- Now differentiating the revenue with respect to x, we get:
dR/dx = 1750 - 100x
1750 - 100P = 0
x = 17.5
d²R/dx² = - 100
d²R/dx² < 0
- So the maximum revenue at x is 17.5
- But x should be integer, so consider 17 and 18, we get:
- Revenue = (200 - 5x)(50 + 10x)
- If x = 17
- Then Revenue will be:
= (200 - 85) (50 + 170)
= 25300
- If x = 18
- Then Revenue will be:
= (200 - 90) (50 + 180)
= 25300
- So the passengers will be 220 or 230 will maximize the revenue of the operator.
- And if we consider 17.5, then Revenue will be:
= (200 - 87.5) (50 + 175)
= 25312.5
Passengers = 225
Answer:
So the number of passengers will be 220 to 230.
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
where
Thus, the revenue
For Max R
Now,
Hence at 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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