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 $$1,200,$ while the low fare is $$500.$ Buy up probability is $0\mathrm{.}3.$

What is the protection level for the high$-$fare class? $[$ Select $]["15","16","17","18","19","20"]$

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

$($a$)$ Capacity $=100$ seats? $[$ Select $]["80","81","82","83","84","85"]$

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