On a certain route, an airline carries 5,000 every month. Each passenger pays $400 for a ticket. Research predicted that every time the ticket went up $10 in price, the airline would lose 100 passengers. What should the airline charge to maximize their revenue?
Thanks in advance.
Thanks in advance.
-
I think there's a formula to solve this, but I could not remember it. However, the brute force approach could be applied, since there's not too many iterations.
at $400, 5,000 passengers would be our base line.
Thus,
$400 x 5000 = $2,000,000
$410 x 4900 = $2,009,000
$420 x 4800 = $2,010,600
$430 x 4700 = $2,021,000
$440 x 4600 = $2,024,000
$450 x 4500 = $2,025,000 ------------> this is when the revenue is maximum
$460 x 4400 = $2,024,000
$460 x 4300 = $2,021,000
...
Thus, the ticket price would be $450
at $400, 5,000 passengers would be our base line.
Thus,
$400 x 5000 = $2,000,000
$410 x 4900 = $2,009,000
$420 x 4800 = $2,010,600
$430 x 4700 = $2,021,000
$440 x 4600 = $2,024,000
$450 x 4500 = $2,025,000 ------------> this is when the revenue is maximum
$460 x 4400 = $2,024,000
$460 x 4300 = $2,021,000
...
Thus, the ticket price would be $450
-
$450