Arts Centre Parking

It is said that "Australia has one of the world's great opera houses; unfortunately, the outside is in Sydney and the inside is in Melbourne."

The opera house in Melbourne is called the Arts Centre, and it has 250 seats. Demand for a typical opera is Q = 400 - 2P, but there is only demand so long as the opera patrons can park for free beneath the Arts Centre. (Opera patrons are lazy, and don't like to walk. They are also selfish, so each patron drives in a car all by himself or herself.)

There are 300 parking places beneath the Arts Centre, and the parking is owned and operated by the Arts Centre. Suppose there are no other uses for the parking places.

What price do you charge for the opera tickets?

Assume that the Arts Centre is very conveniently located in the middle of town, so its parking lot is very popular. They can sell as many parking places as they want for $20 per night. However, a Melbourne city ordinance prohibits them from charging more than $20 per night for parking. The system at the Arts Centre is to allow opera patrons to park for free, if they show their ticket, and to allow a certain number of "outside people" (non-opera-attenders) to park at $20 per night.

How many parking places do they set aside for "outside people", on an opera night?

Suppose that the very popular opera "Carmen" is showing tonight. Demand for that opera is Q = 600 - 2P. How many parking places does the Arts Centre allow "outside people" to use, now?

Now what is the price of an opera ticket?