Suppose that the first $($high$-$fare$)$ class demand is uniform between $10$ and $30$ seats on a flight. Moreover, first$-$class passengers pay $$1,200,$ while the low fare is $$500.$ Buy up probability is $0\mathrm{.}3.$

What is the protection level for the high$-$fare class?

What are the booking limits for the low$-$fare class if the flight has:

$($a$)$ Capacity $=100$ seats

$($b$)$ Capacity $=30$ seats?