Problem $5.$ You own a private parking lot near Stony Brook University with a capacity of $600$ cars. The demand

for parking at this lot is estimated to be $q=1000-2p$ where $q$ is the number of costumers with monthly parking

passes and $p$ is the monthly parking fee per car. $(20)$

$($a$)$ Derive your Marginal Revenue schedule.

$($b$)$ What price generates the greatest revenues?

$($c$)$ Your fixed costs of operating the parking lot, such as the monthly lease paid to the landlord and the cost of

hiring an attendant, are $$25,000$ per month. In addition, your insurance company charges you $$20$ per car per

month for liability coverage, and the city of Brookhaven charges you $$30$ per car per month as part of its

policy to discourage the use of private automobiles. What is your profit$-$maximizing price?