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 ?
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 $