On a certain route, an airline carries 8000 passengers per month, each paying $50. A market survey indicates that for each $

Question

2 years ago

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On a certain route, an airline carries 8000 passengers per month, each paying $50. A market survey indicates that for each $

1 increase in the ticket price, the airline will lose 100 passengers. Find the ticket price that will maximize the airline's monthly revenue for the route. What is the maximum monthly revenue?

Mathematics

1 answer:

Jobisdone [24] · Answer 1 · 2023-02-06T01:21:47+03:00

Answer:

$65
$424500

Step-by-step explanation:

Let x be the price increase.

Then the current price is:

50 + x

Then the number of passengers is:

8000 − 100x

Then the revenue:

Revenue = Price * Number of Passengers
R = (50 + x)(8000 − 100x) =
- 100x² + 3000x+ 400000

This is a quadratic relationship. Maximum point is obtained at vertex.

Vertex is determined by x = - b/2a, find the value of x:

x = - 3000 / (-2*100) = 15

The maximum revenue is:

R = (50 + 15)(8000 − 100 * 15) = 424500

On a certain​ route, an airline carries 8000 passengers per​ month, each paying ​$50. A market survey indicates that for each​ $

On a certain route, an airline carries 8000 passengers per month, each paying $50. A market survey indicates that for each $