economics help?

Question

Suppose that the demand curve for a bridge is,
q = a - bp
where
q=trips per day
p=toll
a,b=positive numbers

Once the bridge is built, the cost to cross it is zero. But to build it costs C. What toll will pay it off? What toll will maximize the net benefits of the bridge?

My math teacher in high school a couple years ago always told me that one day all the numbers would dissapear....i was clearly not ready for this :(

thanks for your help.

Answer 1

The number of trips to pay off is C/p the time it will take is C/(pq)=d days so it will be paid off when C=pqd
This is a confusingly worded problem but to get around the problem of imprecise time let A=ad and B=bd
then
C=Ap-Bp^2 use the quadratic formula to solve for p
note: A^2-4BC must be greater than 0 or a^2d-4bC>0 for a solution
The maximum benefit is for p=0