0

GetThere Airlines currently charges $200$ dollars per ticket,and sells $40,000$ tickets.For every $10$ dollars they increase the ticket price,they sell $1000$ fewer tickets.

How much should they charge to maximize their revenue ?

I am not able to model an equation for the second part of the problem,where the company increases the ticket price for every $10$ dollars.

My guess is that the equation must be some kind of hyperbola but other than that I am quite clueless...

Can someone give me a hint ?

Mr. Y
  • 2,637

1 Answers1

1

Let $x$ be price per ticket and let $y$ be the number of tickets sold. By the given conditions, we have the following equation

$$y= -100x + 60000$$

We want maximize the revenue which is $xy = x(-100x + 60000)$. The maximum of this function occurs at $x=300$. Hence, the maximum revenue is $300*30000=9,000,000$. We can make $\$9M $

chandu1729
  • 3,801
  • Wait,can you explain how you derived these equations ? – Mr. Y Feb 05 '16 at 18:08
  • 1
    For every 10 dollars they increase the ticket price,they sell 1000 fewer tickets which means for every 1 dollar they increase, they sell 100 fewer tickets. I am assuming a linear model since there is no other information. You can just try to write the equation of line passing through (200, 40000) and (210, 39000) – chandu1729 Feb 05 '16 at 18:19
  • In the first equation $y=-100x+20000$ If I substitute $x=200$ I get $y=0$ which can't be possible. – Mr. Y Feb 05 '16 at 18:51
  • There was a mistake. I made the edits. Please check it now – chandu1729 Feb 05 '16 at 19:01