A transit company charges $1.25 per ride with 10 000 passengers a day. The company wants to increase profit but realize that with each 10 cent augmentation in fare, they will lose 500 passengers. What should the company charge to maximize profit?
Profit would maximize at
Let the prices be increased in steps of
But number of passengers will go down by
Now we should have an extrema where first derivative is zero and as it is
Note that second derivative is
Hence, profit would maximize at