Question

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?

Answer 1

• $65
• $424500

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