Answered

IDNLearn.com provides a platform for sharing and gaining valuable knowledge. Discover prompt and accurate responses from our experts, ensuring you get the information you need quickly.

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?

Sagot :

Mhanifaidn

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
We value your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Discover the answers you need at IDNLearn.com. Thank you for visiting, and we hope to see you again for more solutions.