Please can you give some ideas on how to solve the problem, even if you can't help with the final solution..Thank you!
The demand for bus transportation in a small city is P=100-Q, where P is the price of the bus fare, and Q are rides per month (units=10,000 rides).
(a) What is the revenue function for bus rides? Plot this function.
(b) How many rides per month will maximize revenue, i.e., what is the Q value from the revenue function in (a) which maximizes revenue?
(c) What is the demand elasticity at the revenue maximizing level of Q, to the left of this point (rides fewer than the revenue-maximizing level), and to the right of this point (rides greater than the maximizing revenue point?
(d) From your answer in (c) what is the relationship between dR/dQ and the demand elasticity? Note: R is revenue, and Q is rides, so dR/dQ is change in revenue with the number of rides.
(e) Suppose the operating costs of provisioning bus service is: C= 20Q, and the goal of the transportation authority is to maximize revenues less costs (net operating profit). What number of rides maximizes net-operating profit?
(f) Given your answer in (e), what is the bus fare the transportation authority should charge to maximize its net-operating profit
Demand elasticity is found here.