MATH3171 Assignment
Due date: 5 pm on 21/November/2020 (Saturday)
Information of this Assignment
Your answers to this assignment must be submitted via Moodle before 5 pm on 21/Novem-
ber/2020 (Saturday). Late assignments will not be accepted except on documented medical
or compassionate grounds (and need to go through the special consideration process and
obtain approval accordingly). Assignments must include a signed cover sheet (the school
stamp is not needed) available from the School of Mathematics and Statistics web site at :
http://www.maths.unsw.edu.au/sites/default/files/assignment.pdf
Marking of this Assignment
A full mark of 20 on this assignment is worth 10% of the total marks for MATH3171. Present
your work as a self contained, well-written report including the problem statement, solution
summary, model formulation, definition of problem variables and your computer output.
State clearly the assumptions that you make. Any Matlab files that you modify/write
should be included as an appendix.
1. Transportation problem (6 marks)
The company powerco has three electric power plants that supply the needs of four
cities. Each power plant can supply the following number of kilowatt-hours (kwh) of
electricity: power plant I – 30 million; power plant II – 55 million; power plant III –
40 million. The costs of sending 1 million kwh of electricity from plants to cities are
summarized in Table 1. The peak power demands in these cities are as follows (in
kwh): city I – 40 million; city II – 25 million; city III – 30 million; city IV – 30 million.
The company wish to minimize the total cost of sending the electricity from the three
electric power plants to the four cities, and to meet each city’s peak power demand.
City I City II City III City IV
Power Plant I $4 $3 $10 $9
Power Plant II $9 $6 $13 $7
Power Plant III $12 $9 $16 $6
Table 1: Costs of sending 1 million kwh of electricity from plants to cities
1
Formulate this as a linear programming problem and solve it using Matlab. Find out a
global optimal solution, the associated minimal cost and interpret your results. Provide
the Matlab code in the Appendix.
2. CCTV Surveillance Problem (14 marks)
During the past few months, the suburb Surrey has suffered from a series of break-ins
and thefts during the night. The city council of Surrey decides to install surveillance
cameras in this suburb to improve the security. These cameras can be directed and
pivot through 360◦. By installing a camera at the intersection of several streets, it is
possible to survey all adjoining streets. The map in the following Figure shows the
streets need to be covered by the closed circuit TV (CCTV) surveillance and the 49
possible locations where to install the cameras. Here, we interpret a street as the
arc in the map linking two possible locations of the cameras without having a third
possible location of the cameras in between (for example, the arc between location 22
to location 25 is one street, while the arc between location 25 to location 26 is another
street).
2
The costs of installing a new cameras at the possible locations 1− 49 are listed in the
following table 1:
Location Cost (1 new camera+installation fees)
Location 13 $ 1000
Location 41 $ 1000
other locations $ 800
The city council would like to minimize the total cost of installing cameras and make
sure every street can be surveyed by at least one camera.
(a) Formulate this CCTV surveillance problem as an integer programming problem
and solve it using Matlab. Find out where these cameras should be placed and
what are the corresponding total cost.
(b) Provide a report explaining the model and the results you obtain in part (a), to
the Mayor of the city council. Provide the Matlab code in the Appendix.
(c) Discuss the model and the associated assumptions of the model.
1The locations 13 and 41 link with two main roads connecting Surrey with other suburbs. Therefore,
higher quality of cameras are needed for these two locations.
3

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