Springfield Airways is looking to optimize its reservation systems and has asked Lisa to help figure this out.

The airline can sell as many seats ahead of time as it wants to at $184 per ticket.

However, the airline can charge business travelers who book at the last minute (like C. Montgomery Burns) as much as $771 per ticket.

Springfield Airways doesn't know how many business travelers will arrive at the last minute. It knows that whatever seats it protects will either be filled at the last-minute rate of $771/ticket or stay empty. Assume the airline won't dynamically change the fare back down to $184 if not enough last-minute fliers show up - it is thinking of the long game, and once those seats are protected at the high fare, it won't change them back.

On the other hand, if the airline doesn't protect enough high-priced last-minute seats and instead fills up too many advance seats at $184, it will miss out on a significant revenue opportunity to make substantial profits from business travelers like Mr. Burns.

The airline hires Lisa to determine the correct number of seats to reserve to balance these possibilities. They tell Lisa that while business traveler demand is uncertain, it has a normal distribution with a mean of 52 and a standard deviation of 6.

What is the under-stocking cost Cu?

What is the over-stocking cost Co?

What is the critical fractile? Please state your answer as a number between 0 and 1, round to 4 decimal places.

What is the corresponding z-score?

How many seats should Springfield Airways protect for these last-minute travelers? Enter a whole numberdon't use fractions or decimals. Round up, round down, or whatever you like. The airline doesn't mind either way