1.
(a)
[2 marks]
Define the term
extreme point
.
Now consider a system of constraints
Ax
=
b
x
≥
0
.
Suppose that the vector [2
,
3
,
0
,
4
,
0]
T
is a basic feasible solution, and that the vector
[0
,
1
,
2
,
2
,
4]
T
is a feasible solution that may or may not be basic. Answer the following
questions,
justifying your answers carefully
.
(b)
[2 marks]
Exactly one of the following statements is correct. State which one, and
explain why it is correct.
(i)
A
must have no more than 3 rows.
(ii)
A
must have at least 3 rows.
(c)
[2 marks]
Find an extreme point of the feasible region.
(d)
[2 marks]
Find a feasible solution that is not an extreme point of the feasible
region.
1
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2.
[6 marks]
Use the simplex method to solve the linear program
maximize
x
1

x
2

x
3
subject to
2
x
1
+
x
2

x
3
≤
2
3
x
1
+
2
x
2
≤
4

x
1
+
x
3
≤
0
x
1
,
x
2
,
x
3
≥
0
.
At each iteration, list the basic variables, the corresponding basic feasible solution, its
objective value, and the entering and leaving variables.
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 '10
 TODD
 Linear Programming, Optimization, feasible solution, basic feasible solution

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