Suppose that the first $($high$-$fare$)$ class demand is normal with a mean of $15$ seats and a standard deviation of $4.$ Moreover, first$-$class passengers pay $$900,$ while the low fare is $$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?