Problem#$1$

$($Overbooking Problem$)$

A family$-$run inn is considering the use of overbooking, because the frequency of no$-$shows listed below has left many rooms vacant during the past summer season. An empty room represents an opportunity cost of $$69,$ which is the average room rate. Accommodating an overbooked guest is expensive, however, because the nearby resort rooms average $$119$ and the inn must pay the difference. What would be the expected gain per night from overbooking?

$\backslash$table$[[$No$-$shows,$0,1,2,3],[$Frequency$,4,3,2,1]]$

$\backslash$table$[[$No Show,Probability,Reservation Overbooked$],[0,1,2,3],[0,,0,,,],[1,,,0,,],[2,,,,0,],[3,,,,,0],[\backslash$table$[[$Expected$],[$Loss$]],1,,,,]]$