Please can you provide some ideas on how to solve the problem, even if you can't help with the final solution..
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).
Question 1: What is the revenue function for bus rides? Plot this function.
Question 2: How many rides per month will maximize revenue, i.e., what is the Q value from the revenue function in (a) which maximizes revenue?
Question 3: 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?
Question 4: 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.
Question 5: 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?
Question 6: Given your answer in (e), what is the bus fare the transportation authority should charge to maximize its net-operating profit.