IELM 202, Assignment #3
Due date: 26 October 2005, Wednesday, 12:00 noon
Question 1 (20 marks):
Consider the primal problem as below:
Maximize
Z = 2x
1
+ x
2
Subject to:
x
2
≦
10
2x
1
+ 5x
2
≦
60
x
1
+
x
2
≦
18
3x
1
+
x
2
≦
44
and
x
1
≧
0, x
2
≧
0
a).
Construct the dual problem
b).
Use the fact that (x
1
, x
2
) = (13, 5) is optimal for the primal problem to identify the
nonbasic variables and basic variables for the optimal basis solution for the dual
problem.
Question 2 (30 marks)
:
Consider the primal problem as below:
Maximize Z = 3x
1
+ 7x
2
+ 2x
3
Subject to:
2x
1
+ 2x
2
+ x
3
≦
10
3x
1
+
x
2

x
3
≦
20
and
x
1
≧
0, x
2
≧
0, x
3
≧
0
a).
Construct the dual problem
b).
Solve the dual graphically
c).
Find out the primal solution
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View Full DocumentQuestion 3 (30 marks):
One of Speedy Airlines’ flights is about to take off from Seattle for a nonstop flight to
London. The flight has to pass through several intermediate air control stations to keep
track the flight. There is some flexibility in choosing the precise route to be taken,
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 Fall '10
 D
 Shortest path problem, Seattle, air control stations, intermediate air control, Speedy Airlines

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