Homework answers / question archive / eee cae (erAy hag se vs f eederound: Sk Fax Allin (STAY has hired you as'a consultant and hopes you can help thers: aa a ee : ie “ohm ntains a 10-aircraft fleet of Boeing 737’s which they fly out of Hartford

eee cae (erAy hag se vs f eederound: Sk Fax Allin (STAY has hired you as'a consultant and hopes you can help thers: aa a ee : ie “ohm ntains a 10-aircraft fleet of Boeing 737’s which they fly out of Hartford

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eee cae (erAy hag se

vs f eederound: Sk Fax Allin (STAY has hired you as'a consultant and hopes you can help thers: aa
a ee
: ie “ohm ntains a 10-aircraft fleet of Boeing 737’s which they fly out of Hartford. A Boeing 737.5
Gy eh telntains 2 10-aircraf flee "seating scheme (Le. there is only one seating class). ae
ao _ Gan seat 189 passengers in an “economy” seating scl eme (i.e., there is only one seating a SS)
 stactarees low fares and flies to smaller regional airports. ' a ee
ae | | ic
| STA wants to maximize its revenue for each flight. The problem is no-shows — customers who as
. ‘buy tickets but who don’t show up for their flight. Each no-show creates an empty seat which
| could be used by another paying passenger. | as
=... Records of flights over the last 10-years suggest 92.5% of passengers who purchase a ticket for ~~
eee _. 4 flight actually do show up for the flight (equivalently, there is a 7.5% no-show rate). nee
== For the purposes of this project, you can assume that the show rate is constant, and that an.
ee _ whether a given passenger shows for a flight is independent of what other passengers decide to =
So 1. Let X be a random variable counting the number of passengers who purchase aticket — ee
ee for a flight and show up for the flight. If 189 tickets are sold, X is modeled byabinomial - =
is random variable. That is, X ~ B(n, p). What are the values of n and p? — 2
2. For X as above, compute px and ox. er
a _ 3. IFSTA sells 189 tickets for a flight, how many passengers do you expect to show upfor
._ 4. Still assuming that 92.5% of passengers who purchase a ticket fora flight actually do aa
Se show up for the flight, complete the following table using Excel: ake

eee ~~ f= number of tickets sold ee
ae mu = number of passengers expected to show up given n tickets sold. “22a
ee a
a P(X >= 190) = probability that more than 189 of the n Passengers who purct ase
. ' tickets show up for the flight (i.e., the likelihood of having to bump someone} | =m
The table should contain enough rows beyond 190 in order to find an n value so that” 758

round(mu) for that n is 189. es
As a check-point for your table, when n = 200, mu = 185 and P(X >= 190) = 0.10915429,
~... 5. Based on the information in the table from question 4, STA would like you to. = es
a recommend an overbooking policy. _ 0 Spa
Ba ~ Tickets cost $150. In addition, the FAA fines airlines $10000 if they overbook a flight and == =
=~ . bump 1or more passengers. Revenue for a given n value is modeled by: oo. >
=~ R= 150%mu — (10000 ~ 150*(189 - mu))*P(X >= 190) ee
===. Breaking this down, 150*mu is the revenue generated by the expected number of. == aes
= -—- _ passengers for a given n. 10000 — 150*(189 — mu) is the FAA fine adjusted by the extra: 2 es
[=~ revenue earned if the flight is overbooked (since 189 — mu more tickets willbe: 38 ae
5 redeemed for the flight). (10000 — 150*(189 — mu))*P(x >= 190) is the probability: jaa
[= weighted value of the adjusted fine for overbooking and bumping 1 or more paSsen aaa

ae Add a column for revenue R to your table from question 4, and compute. thie: sean
| er la for R above. i

fn pe eect elven n using the formula fo - ee Me

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