The Curtis M Philips Center for the Performing Arts at UF is staging Hamilton on a specific night in May 2023. With a fixed capacity of 1700 seats in the proscenium hall, the focus is on maximizing occupancy for the show.

Based on historical data, it is estimated that if the seats are offered at a low price of $ pL=25 per seat, all 1700 seats will be sold. The Center 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.

To start with, showing all supporting analytics, complete the following table.

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 expected total profit?

\begin{tabular}{|l|l|l|l|l|l|l|} \hline HighPrice & Protectionlevel(seats) & Bookinglimit(seats) & DemandLost(seats) & ExpectedSalesathigh-rate(seats) & CapacityUtilization(%) & ExpectedTotalProfit($) \\ \hline$50 & & & & & & \\ \hline$75 & & & & & & \\ \hline$100 & & & & & & \\ \hline \end{tabular}