On a given GNV$-$ATL flight, there are $200$ seats and each seat is sold at an average ticket On a given GNV$-$ATL flight, there are $200$ seats and each seat is sold at an average ticket price of $$250.$ It has been observed that on most days in the past month, the flight rarely approaches $100\%$ occupancy since there are passenger no$-$shows. Hence, the airline decides to overbook flights. The airline manager assigned the task of determining the number of seats to overbook on this flight starts by estimating no$-$shows using historical information. However, she encounters an interesting conundrum: the mean no$-$shows changes based on the rate offered to customers with a confirmed booking who are denied a seat on the flight $($referred to as the service denial rate$).$

She would like to start by analyzing the impact of an overbooking policy by considering three specific service denial rates:

Service Denial Rate $=$$$400.$ No$-$shows for this denial rate are uncertain and normally distributed with a mean $=25$ and standard deviation $=7.$

Service Denial Rate $=$$$500.$ No$-$shows for this denial rate are uncertain and normally distributed with a mean $=22$ and standard deviation $=8.$

Service Denial Rate $=$$$600.$ No$-$shows for this denial rate are uncertain and normally distributed with a mean $=19$ and standard deviation $=9.$

You are required to:

Complete the following table showing all supporting analytics.

$\backslash$table$[[\backslash$table$[[$Service$],[$Denial$],[$Rate$]],\backslash$table$[[$Optimal$],[$Overbooks$],[$Y$*],[($seats$)]],\backslash$table$[[$Percentage$],[$of time$],[$passengers$],[$with a$],[$confirmed$],[$reservation$],[$will be$],[$denied a seat$],[(\%)]],\backslash$table$[[$Expected$],[$number of$],[$passengers$],[$with a$],[$confirmed$],[$reservation$],[$who will$],[$be denied a$],[$seat$]],\backslash$table$[[$Expected$],[$Loss from$],[$denying a$],[$seat to$],[$passengers$],[$with a$],[$confirmed$],[$reservation$],[($$$)]],\backslash$table$[[$Expected$],[$number$],[$of empty$],[$seats$]],\backslash$table$[[$Expected$],[$loss from$],[$empty seats$],[($$$)]]],[$$$400,,,,,,],[$$$500,,,,,,],[$$$600,,,,,,]]$

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

Which service denial rate should be chosen if the manager wants to minimize the percentage of time customers with a confirmed reservation will be denied a seat?

Which service denial rate should be chosen if the manager wants to minimize the expected Loss from denying a seat to passengers with a confirmed reservation?

price of $ $250.$ It has been observed that on most days in the past month, the flight rarely

approaches $100\%$ occupancy since there are passenger no$-$shows. Hence, the airline

decides to overbook flights. The airline manager assigned the task of determining the

number of seats to overbook on this flight starts by estimating no$-$shows using historical

information. However, she encounters an interesting conundrum: the mean no$-$shows

changes based on the rate offered to customers with a confirmed booking who are denied

a seat on the flight $($referred to as the service denial rate$).$

She would like to start by analyzing the impact of an overbooking policy by considering

three specific service denial rates:

$1.$ Service Denial Rate $=$$ $400.$ No$-$shows for this denial rate are uncertain and

normally distributed with a mean $=25$ and standard deviation $\backslash$sigma $=7.$

$2.$ Service Denial Rate $=$$ $500.$ No$-$shows for this denial rate are uncertain and

normally distributed with a mean $=22$ and standard deviation $\backslash$sigma $=8.$

$3.$ Service Denial Rate $=$$ $600.$ No$-$shows for this denial rate are uncertain and

normally distributed with a mean $=19$ and standard deviation $\backslash$sigma $=9.$

You are required to:

$1.$ Complete the following table showing all supporting analytics.

$2.$ Based on the results in the table, answer the following questions:

$$ Which service denial rate should be chosen if the manager wants to minimize the

percentage of time customers with a confirmed reservation will be denied a seat?

$$ Which service denial rate should be chosen if the manager wants to minimize the

expected Loss from denying a seat to passengers with a confirmed reservation?