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MAP602S - MATHEMATICAL PROGRAMMING - 1ST OPP - NOVEMBER 2024 |
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nAmlBIA UnlVERSITY
0 F SCIEnc E Ano TECHn OLOGY
FacultyofHealthN, atural
ResourceasndApplied
Sciences
Schoool f NaturalandApplied
Sciences
Departmentof Mathematics,
Statisticsand Actuarial Science
13JacksonKaujeuaStreet
PrivateBag13388
Windhoek
NAMIBIA
T: +264612072913
E: msas@nust.na
W: www.nust.na
QUALIFICATION: BACHELOR OF SCIENCE IN APPLIED MATHEMATICS AND STATISTICS
QUALIFICATION CODE: 07BSAM
LEVEL: 6
COURSE: MATHEMATICAL PROGRAMMING
COURSECODE: MAP602S
DATE: NOVEMBER 2024
SESSION: 1
DURATION: 3 HOURS
MARKS: 100
EXAMINER:
MODERATOR:
FIRST OPPORTUNITY: EXAMINATION QUESTION PAPER
Mr Benson.E Obabueki
Prof 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. All written work must be done in blue or black ink and sketches in pencil.
7. Show clearly all the steps used in the calculations.
PERMISSIBLE MATERIALS:
1. Non-Programmable Calculator without a cover.
2. Graph paper to be provided by the Examinations Department.
ATTACHEMENTS
None
This question consists of 2 pages excluding this front page
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Question 1 (13 marks)
A landscaper wants to mix her own fertilizer containing a minimum of 50 units of phosphates,
a maximum of 240 units of nitrates, exactly 210 units of calcium and some amount of
Potassium. The amount of potassium cannot be more than twice the amount of phosphates
and nitrates combined. Brand 1 contains 1 unit of phosphates, 6 units of nitrates, 15 units of
calcium, and 8 units of potassium. Brand 2 contains 5 units of phosphates, 8 units of nitrates
and 6 units of calcium. Brand 1 costs $250 per kilogramme; brand 2 costs $500 per kilogramme.
Model this information into a linear program. You must define your variables unambiguously
and mention your constraints.
(13)
Question 2 (15 marks)
Solve the following linear programme graphically. Use a scale of 1cm to 1 unit on both axes.
Maximize H =l5x+9y
Subject to l Ox+ lOy 100
8x+Sy2 40
(15)
4x+8y232
x22
y20
Question 3 (30 marks)
Consider the following minimization linear programme:
Minimize M = l2x+ lOy
Subject to
8x + 5y 2 40
4x+8y232
x22
y2l
3.1 Write down the dual of the linear programme.
(S)
3.2 Solve the dual completely.
(11)
3.3 Use the solution of the dual to solve the given minimization programme.
(14)
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Question 4 {22 marks)
A businessman gets a product from three sources 51, 52, and 53 to his four business locations
D1, D2, D3, and D4. The cost of transporting one unit of the product from the sources to the
destinations, together with the capacity of each source and order for each destination are
given in the following table:
01 02 03 04 Supply
51
8 10 9 11
110
52
9 12 14 10
100
53
8 11 15 16
130
Demand 80 90 100 120
4.1 Balance the problem/table.
(2)
4.2 Use the Vogel Approximation Method to obtain the initial solution. Where there is a
tie among cells, you must allocate to the cell that is most North-Westerly among the
tying cells.
(7)
4.3 Use the Modified Distribution Method to obtain the optimum solution.
(13)
Question 5 {12 marks)
Maria has four workers Wl, W2, W3, and W4. Any of these workers can perform any of the
tasks Tl, T2, T3, and T4. The costs of assigning the workers to the tasks are given in the table
below. Use the Hungarian method to assign the tasks in order to minimize assignment total
costs?
Tl T2 T3 T4
Wl
28 30 35 40
W2
50 38 38 45
W3
40 45 45 55
W4
so so 48 55
(12)
End of paper
Total marks: 92, convertible to 100
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