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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?

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
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