NATIONAL UNIVERSITY OF SINGAPORE
Department of Mathematics
MA3252 Linear and Network Optimization
Tutorial 10
1. Adam and Eve are planning a drive from location A to E. The time to travel and the
scenic rating for the roads in the network are given below. All roads are oneway.
Adam wants to reach location E as fast as possible while Eve wants to take the
most scenic drive to location E (a higher scenic rating implies a prettier scene).
Road
Time (hours)
Scenic Rating (points)
A to B
3.0
3
A to C
2.5
4
B to D
1.7
5
B to E
2.8
7
C to B
1.7
4
C to F
2.5
3
D to E
2.0
9
F to E
2.0
8
(a) Formulate the linear programs that Adam and Eve need to solve respectively.
Do you think they can find a common optimal driving route?
(b) Suppose Eve agrees to use Adams least time policy under the condition that
they will take the highly scenic road D to E. How would you modify Adams
linear program in this case?
(c) Suppose Adam and Eve need to pick up John from location C on their drive
from A to E. How would you modify Adams linear program in this case?
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 Spring '10
 TanBanPin
 Math, Optimization, Shortest path problem, Eve, Adam and Eve, scenic rating

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