$(20)$ Demand for Desert View campground is $P=100-0\mathrm{.}5x($ X is overnight occupied sites.$)$ Marginal cost to supply campsites is constant at $$50($MC$=$ATC$)$ and there are $50$ campsites.

a$.$ Find the efficient number of campsites used and overnight fee to charge.

b$.$ Does the campground generate a profit, loss, or breakeven at the fee calculated in part $($a$).$

c$.$ Suppose the campground is required to set a price to just cover its average costs $($i$.$e$.,$ zero profit.$)$ At this price, what is the wait list on weekends? How can managers most efficiently ration demand?