$1.(30$ points$)$ The typical golfer at Bushwood Country Club has the following inverse demand for rounds of golf at the club per year:$$ P $=1001\mathrm{.}5$Q$.$ For every round of golf played, Bushwood incurs a marginal cost of $$10.$

Judge Smails, the club president, wants to charge a single monopoly price for each round of golf at Bushwood. How many rounds of golf will the typical golfer play and what is the price per round?$$ How much profit will the club obtain from a typical golfer?

Danny Noonan, the club$$s top caddy, believes he has a better idea. He suggests a two$-$part pricing system that includes a membership fee and a fee for each round of golf played. What should the membership fee and per round fee be$?$ How many rounds of golf will the typical golfer play? What is the club$$s profit from each golfer now?

If golfers vary in their demand for golf from the typical golfer, how will that make Danny Noonan$$s idea less effective?