Problem $3(2$ pts$)$ Consider a flight from Houston to Istanbul. The ticket price is $p=$$$220,$ the flight capacity is C $=120$ and overbooking limit is $b=128.$

a$)(1$ pts$)$ Compute the number of accepted bookings and the number of passengers denied boarding for the following scenarios: put these numbers into the table below. If a certain scenario is not possible, put NP in its row.

$\backslash$table$[[$Scenario$,$C$,$b$,$# of requests made,# of show$-$ups,$\backslash$table$[[$Accepted$],[$bookings$]],\backslash$table$[[$Denied$],[$boardings$]]],[1,120,128,125,112,,],[2,120,128,119,108,,],[3,120,128,115,116,,],[4,120,128,126,121,,],[5,120,128,130,123,,]]$

b$)(0\mathrm{.}5$ pts$)$ Suppose that all the possible $($i$.$e$.,$ non NP$)$ rows above happen with equal probability and compute the expected number of accepted bookings and expected number of denied boardings.

c$)(0\mathrm{.}5$ pts $)$ Let $$ be the profit which can be written as

$=p(Numberof$ Accepted bookings$)-D(Numberof$ Denied boardings$).$

Calculate expected profit using the numbers you obtained in part b$)$ if $D=$$$450.$