M1D2 RQ
png
keyboard_arrow_up
School
University of Michigan *
*We aren’t endorsed by this school
Course
301
Subject
Industrial Engineering
Date
Jan 9, 2024
Type
png
Pages
1
Uploaded by CommodoreCaribouMaster1044
Question
1
1/1pts
‘
Which
of
the
following
best
describes
the
solution
to
the
LP
with
the
objective
min
x
+
y
with
the
constraints
x
+y
>=
5,y
>=2,
x
>=0.
‘
Unbounded
feasible
region
with
only
one
optimal
solution
(X)Y)
=
(3,2).
Unbounded
feasible
region
with
no
optimal
solution.
Unbounded
feasible
region
with multiple
optimal
solutions.
Infeasible,
no
solution.
A
first
step
is
to
visualize
or
draw
the
feasible
region.
It
is
unbounded
because
x
and
y
can
take
any
value
as
long
as
they
sum
to
greater
than
5
where
x
is
non-negative
and
y
is
at
least
2.
Next,
you
can
think
about
the
z-line.
The
slope
of
the
z-line
is
-1.
And
the
slope
of
the
first
constraint
is
-1.
The
direction
of
minimization
of
the
objective
function
is
towards
Constraint
1.
They
will
be
co-incident,
creating multiple
optimal
solutions
on
the
line
between
(X)Y)
=
(0,5)
and
(X)Y)
=
(3,2).
1/1pts
Question
2
In
Excel,
you
solve
a
profit-maximizing
LP
with
two
variables
X
and
Y.
Solver
finds
the
optimal
solution
and
you
see
a
value
of
9
in
the
X
solution
cell
and
2
in
the
Y
solution
cell.
You
have
a
resource
that
is
required
for
making
both
X
and
Y.
Every
unit
of
X
variable
uses
up
2
units
and
every
unit
of
Y
uses
up
3
units
of
your
resource.
How
much
of
your
resource
have
been
used
at
the
optimal
solution?
»
.
Plug
in
the
values
of X
and
Y
in
2X+3Y
to
find
the
correct
answer.
Question
3
0/1pts
‘
In
a
linear
program
with
two
decision
variables,
X
and
Y,
which
of
the
following
is
NOT
possible?
m[
Having
an
unbounded
feasible
space
but
a
unique
optimal
solution.
\swer
Having
exactly
two
optimal
solutions
with
different
(X,Y)
values.
Having
an
infeasible
problem.
‘
Having
infinitely
many
(multiple)
optimal
solutions.
|
|
In
an
LP,
if
we
have
multiple
optimal
solutions,
we
have
infinitely
many
of
them.
If
there
are
two
corner
solutions
that
are
optimal,
all
points
connecting
those
two
solutions
are also
optimal.
It
is
possible
to
have
a
unique
optimal
solution
(or
even
multiple
optimal
solutions)
for
an
LP
with
an
unbounded
feasible
space
if
the
objective
function
does
not
improve
in
the
direction
of
unbounded
region.
An
over-constrained
LP
can
be
infeasible.
Discover more documents: Sign up today!
Unlock a world of knowledge! Explore tailored content for a richer learning experience. Here's what you'll get:
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help