The college basketball tournament is set to begin in March. With a fixed capacity of 1700 seats in the basketball arena, the focus is on maximizing occupancy for the tournament.

Historical data shows that if the seats are offered at a low price of $ pL=25 per seat, all 1700 seats will be sold. The arena is also contemplating offering one of three high prices for the same seats: $ p2=50 per seat, $ p2=75 per seat, or $ p2=100 per seat. Demand at each of these high prices (i.e., p2) is normally distributed such that: if the high rate of $ 50 is offered, then =1000 and =300; if the high rate of $ 75 is offered, then =900 and =300; and if the high rate of $ 100 is offered, then =800 and =300.

Show all calculations and complete the table below.

High Price	Protection level (seats)	Booking limit (seats)	Demand Lost (seats)	Expected Sales at high- rate (seats)	Capacity Utilization (%)	Expected Total profit ($)
$ 50
$ 75
$ 100

Based on the results in the table, answer the following questions:

1. Which high price should be chosen if the manager wants to offer the maximum number of seats to those willing to pay the low price of $ 25?
2. Which high price should be chosen if the manager wants to minimize the demand lost (in seats)?
3. Which high price should be chosen if the manager wants to maximize capacity utilization?
4. Which high price should be chosen if the manager wants to maximize the expected total profit?