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MAP602S - MATHEMATICAL PROGRAMMING - 2ND OPP - JANUARY 2024 |
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n Am I BI A u nI VE Rs ITY
OF SCIEnCE AnOTECHnOLOGY
Facultyof Health,Natural
ResourceasndApplied
Sciences
Schoool f NaturalandApplied
Sciences
Departmentof Mathematics,
StatisticsandActuarialScience
13JacksonKaujeuaStreet
PrivateBag13388
Windhoek
NAMIBIA
T: •264 612072913
E: msas@nust.na
W: wwv1.nust.nJ
QUALIFICATION: BACHELOR of SCIENCE IN APPLIED MATHEMATICS AND STATISTICS
QUALIFICATION CODE: 07BSAM
LEVEL:6
COURSE:MATHEMATICAL PROGRAMMING
COURSECODE: MAP602S
DATE: JANUARY 2024
SESSION: 1
DURATION: 3 HOURS
MARKS: 100
SECONDOPPORTUNITY/SUPPLEMENTARYE:XAMINATIONQUESTIONPAPER
EXAMINER:
MODERATOR:
Mr. Benson E. Obabueki
Professor Adetayo S. Eegunjobi
INSTRUCTIONS:
1. Answer all questions on the separate answer sheet.
2. Please write neatly and legibly.
3. Do not use the left side margin of the exam paper. This must be allowed for the examiner.
4. No books, notes and other additional aids are allowed.
5. Mark all answers clearly with their respective question numbers.
6. Show all your working/calculation steps.
PERMISSIBLE MATERIALS:
1. Non-Programmable Calculator.
2. Metric graph paper to be supplied by examination department.
ATTACHEMENTS
1. None
This paper consists of 2 pages excluding this front page.
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Question 1 (10 marks)
A factory employs unskilled workers each earning N$1350 per week and skilled workers each
earning N$2700 weekly. It is required to keep the weekly wage not above N$243000. The
machines require a minimum of 110 workers, of whom at least 40 must be skilled. Union
regulations require that the number of skilled workers should be at least half the number of
unskilled workers.
Model the above statement into a linear programme. You must clearly define your variables
unambiguously and name your constraints. DO NOTSOLVE.
(10)
Question 2 (13 marks)
Using a scale of 2cm to 1 unit, solve the following linear program graphically:
Maximize T=I0x+3y
Subject to 12x+4y::;; 48
6x+8y::; 48
(13)
2x+5y 10
O=:;y<5
x~O
Question 3 (26 marks)
Consider the primal linear program:
Minimize T =40a +32b
Subject to 6a + 8b 12
8a+6b 14
a,b 0
3.1 Write down the dual of the linear program.
(5)
3.2 Solve the dual of the linear program completely using the simplex method.
(12)
3.3 Use the solution of the dual to determine the solution of the primal program. (9)
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Question 4 {14 marks)
Solve the following linear program using the Big-M method:
Minimize T = 32a + 34b
Subject to 4a+8b 2::12
8a+4b 2::14
(14)
a,b 2::0
Question 5 (20 marks)
A brewing company has three plants that produce Soul-Ale. The products are moved from the
plants to four warehouses. The costs of moving a crate of 50 bottles from each plant to the
different warehouses, the capacities of the plants as well as the demand from the warehouses,
are given in the following table:
Wl W2
Pl
10
2
P2
12
7
P3
4
14
Demand 28
15
W3
W4
Supply
20
11
25
9
20
25
16
18
40
12
15
Use the Vogel Approximation Method to distribute the products in such a way that the total
cost of transportation is minimal.
(20)
Question 6 {17 marks)
A construction company has four large bulldozers located at four different garages. The
bulldozers are to be moved to four different construction sites. The distances in kilometres
between the bulldozers and the construction sites are given below:
BuIIdozer/Site Sl S2 S3 S4
Bl
90 75 75 80
B2
35 85 55 65
B3
125 95 90 105
B4
45 110 95 115
Use the Hungarian method to determine how the bulldozers should be moved to the
construction sites in order to minimize the total distance covered?
(17)
End of paper
Total marks: 100
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