A tour bus in jaipur serves 400 customers a day.the charge is rs 50 per person the owner of the bus services estimates that the company would lose 10 passengers a day for each rs 5 fare increases
Answers 2
Answer:
Step-by-step explanation:
i) Let x represent the number of Rs 5 fare
increases. Then 50 + 5x is the price per
passenger and 400 - 10x is the number of
passengers.
The income is the number of passengers multiplied by the price per ticket. Let I x( )
represent income as a function of x .
Now I x( ) = ( ) 400 − + 10x x ( ) 50 5
= 10( ) 40 − + x x ( )5 1( ) 0
= 50( ) 40 − + x x ( ) 10
50( ) 400 40x x 10 x = + − − 2
50( ) 400 30x x = + − 2
50( ) x x 30 400 =− −2 −
50( ) x x 30 15 15 400 =− −2 2 +−−2
50( ) x x 30 15 625 =− −2 2 + −
50( ) x x 30 15 50 625 2 2 =− − + + #
50( ) x 15 31250 =− − 2 +
(ii) From above equation it is clear that I x( ) is
maximum at x = 15 and this maximum value
is 31250. This means the company should
make 15 fare increases of Rs 5 to maximize
its income. Thus, the ticket price should be
50 + 5 1 # 5 = 125 Rs
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Author:
shrinkwrapsptn
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Q- A tour bus in Jaipur serves 400 customers a day. The charge is Rs 50 per person. The owner of the bus service estimates that the company would lose 10 passengers a day for each Rs 5 fare increase. A. How much should the fare be in order to maximize the income for the company? B. What is the maximum income the company can expect to make?
Answer: The fare should be Rs. 125 and the maximum income is
Rs. 31250
Given,
Total costumers = 400
The charge per person = Rs. 50
The company would lose 10 passengers a day for each Rs 5 fare increase
To Find,
The fare be in order to maximize the income for the company =?
The maximum income the company can expect to make =?
Solution,
Let the number of times the fare increases be x
Then, the total costumers will be 400 - 10x
The charge per person = Rs. 50 + 5x
The total income = l(x) = (400 - 10x)(50 + 5x)
l(x) = 10(40 - x)5(10 + x)
l(x) = 50(400 + 40x - 10x - x²)
l(x) = 50(400 + 30x - x²)
l(x) = -50( x² - 400 -30x + 15² - 15²)
l(x) = -50( x² -30x + 15² - 625)
l(x) = -50(x - 15)² + 50*625
l(x) = -50(x - 15)² + 31250
For maximum income, x should be 15
The company should increase the fare 15 times which means the charge per person
The charge per person = 50 + 5*15 = 50 + 75 = Rs. 125
The maximum income the company can expect to make = Rs. 31250
Hence, the fare should be Rs. 125 in order to maximize the income for the company and the maximum income the company can expect to make is Rs. 31250.
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Author:
simonynfb
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