ORIE 3300/5300
ASSIGNMENT 7
Fall 2008
Individual work.
Due: 3 pm, Friday October 31.
1. Read Section 4.2 (on a multiperiod production model) in the AMPL
book. Read through the problem described in question 45. Do parts
(a) and (b), and save your work (perhaps by putting it in an email to
yourself): you will use it in a future recitation.
2. Consider the linear program
maximize
c
T
x
subject to
Ax
=
b
x
≥
0
,
where
c
=
2
5
9
0
1
A
=
0
1
1
1

1
1
1
2
0
1
b
=
4
5
.
(a) Is
B
= [3
,
2] a basis?
(b) Write down the matrices
A
B
and
A
N
, and the vectors
c
B
and
c
N
.
(c) Calculate
A

1
B
.
(d) Solve the equations
A
B
u
=
b
for
u
and
A
T
B
y
=
c
B
for
y
.
(e) Use your answers to write down the tableau corresponding to
B
.
(f) What is an optimal solution to the problem?
3. Consider again the problem in Q2. Suppose the current basis is
B
=
[4
,
5]. Calculate the current values of the basic variables, ˆ
x
B
. Perform
one iteration of the revised simplex method from this basic feasible so
lution, using the least index rule for the entering and leaving variables.
OVER
1
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4. Suppose you are given a linear program with variables
x
1
, x
2
, . . . , x
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 Fall '08
 TODD

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