December 16, 2005
Economics 617
Final Exam
1. This exam has four questions.
You have 2 hours and 30 minutes to
write the exam.
2. This is a closedbook exam.
3. If you find any question ambiguous, explain your confusion and make
whatever assumptions you think are necessary to answer the question.
Clearly state any additional assumption you make.
GOOD LUCK!
1
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
1. [An Application of Weierstrass Theorem]
[(a) =10 points, (b) = 20 points, (c) = 20 points]
The primal
(
P
)
and dual
(
D
)
problems in linear programming are written
as follows:
Max
q x
Subject to
Ax
≤
b
and
x
≥
0
⎫
⎬
⎭
(
P
);
Min
y b
Subject to
y A
≥
q
and
y
≥
0
⎫
⎬
⎭
(
D
)
where
q
is
1
×
n, A
is
m
×
n, x
is
n
×
1
, b
is
m
×
1
and
y
is
1
×
m.
Define the set of feasible solutions to the Primal as:
F
(
P
) =
{
x
≥
0
such that
Ax
≤
b
}
and the set of feasible solutions to the Dual as:
F
(
D
) =
{
y
≥
0
such that
y A
≥
q
}
Assume that there is
¯
x
∈
F
(
P
)
,
and there is
¯
y
∈
F
(
D
)
.
Further, assume
that
q
∈
R
n
++
.
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '08
 STAFF
 Economics, Derivative, Optimization, Mathematical analysis, Continuous function, weierstrass theorem, implicit function theorem

Click to edit the document details