How much is charged to maximize revenue. calculus problem?

A certain toll road averages 36,000 cars per day when charging $1 per car. A survey concludes that increasing the toll will result in 300 fewer cars for each cent of increase. What toll should be charged in order to maximize the revenue?

How much is charged to maximize revenue. calculus problem?
Let x be the number of cents we increase the toll.





So an expression for the revenue would be:


(36000 - 300x)(1+.01x)





When we FOIL that expression, we get


36000 + 360x - 300x - 3x^2


-3x^2 + 60x + 36000





So the revenue function looks like this:


f(x) = -3x^2 + 60x + 36000


To find the maximum point, we can take the derivative of this function and find when it equals zero:


f'(x) = -6x + 60


-6x + 60 = 0


-6x = -60


x = 10





So the toll should be increased 10 cents to $1.10.