Optimization
Methods
in
Management
Science
MIT
15.053,
Spring
2013
Recitation
10,
Friday
May
3th,
2013
Problem
1
The
Airfare
Problem
1
.
You
are
trying
to
get
the
cheapest
airfare
that
you
can.
just
called
up
and
found
that
the
ticket
home
will
cost
$400,
and
it
cannot
be
refunded
or
exchanged.
can
also
buy
a
ticket
for
$450,
which
can
be
refunded
for
$430
(and
thus
costs
you
$20).
The
price
of
tickets
will
change
in
one
week,
and
you
will
have
one
more
chance
to
buy
a
ticket.
There
is
a
50%
chance
that
the
ticket
would
cost
$300,
and
a
50%
chance
that
it
would
cost
$600.
What
should
you
do
to
minimize
the
expected
expense?
Write
the
Airfare
problem
as
a
decision
tree,
and
solve
it.
Solution.
The
decision
tree
is:
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Suppose
Tom
is
at
a
carnival
and
while
there
he
sees
a
green
monkey
stuﬀed
animal
that
he
would
like
to
have.
In
order
to
win
the
stuﬀed
monkey
needs
to
play
a
game
that
costs
$1.
In
the
game
there
are
5
shells
and
a
ball
that
is
hidden
behind
one
of
the
shells.
In
order
to
win
the
monkey,
needs
to
pick
the
shell
that
the
ball
is
under.
The
monkey
overall
is
worth
$3.
Assume
in
all
parts
of
this
problem
the
probability
the
ball
is
behind
a
give
shell
is
.2
(i.e.
1
/
#
of
shells)
Part
2.A
Determine
using
a
decision
tree
if
it
is
in
Toms
best
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 Spring '07
 JamesOrli
 Management, Shell, Gerber, Worstcase scenario, WorstCase Scenario series

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