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MAP602S - MATHEMATICAL PROGRAMMING - 2ND OPP - JAN 2023 |
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r
nAmlBIA UnlVERSITY
OF SCIEn CE Ano TECHn OLOGY
FACULTYOF HEALTHAND APPLIEDSCIENCES
DEPARTMENT OF MATHEMATICS AND STATISTICS
QUALIFICATION: Bachelor of science in Applied Mathematics and Statistics
QUALIFICATION CODE: 07BSAM
LEVEL: 6
COURSE CODE: MAP602S
COURSE NAME: MATHEMATICAL PROGRAMMING
SESSION: JANUARY 2023
DURATION: 3 HOURS
PAPER:THEORY
MARKS: 100
SUPPLEMENTARY/SECONDOPPORTUNITYQUESTIONPAPER
EXAMINERS
MR. B.EOBABUEKIM, R J AMUNYELA
MODERATOR:
PROFESSORADETAVO EEGUNJOBI
INSTRUCTIONS
1. Answer ALL questions in the booklet provided.
2. Show clearly all the steps used in the calculations.
3. All written work must be done in blue or black ink and sketches must
be done in pencil.
PERMISSIBLEMATERIALS
1. Non-programmable calculator without a cover.
THIS QUESTION PAPER CONSISTS OF 3 PAGES (Excluding this front page)
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Question 1 (10 marks)
A landscaper wants to mix her own fertilizer containing a minimum of 50 units of phosphates,
240 units of nitrates and 210 units of calcium. Brand 1 contains 1 unit of phosphates, 6 units of
nitrates and 15 units of calcium. 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 programming problem. Declare your variables
unambiguously and name the constraints. DO NO SOLVE.
(10)
Question 2 (13 marks)
Solve the following minimization problem graphically. Use a scale of 1cm to 25 units on the x-axis
and a scale of 1cm to 5 units on the y-axis.
(13)
Minimize C = 20x+ 30y
Subject to 9x+ l00y 4500
3x+ 20y::;; 1200
15000::; 75x + 200 y
y::;; 60
X; y ~0
Question 3 (29 marks)
Consider the following L-P model:
Minimize Z = 240x+I20y
Subject to 4x + 8y 56
2x+2y~24
3x+ y 18
x~0;y~0
3.1 Write down the dual of the model.
(5)
3.2 Solve the dual model.
{14)
3.3 Suppose the solution of the dual model is a= 0 ; b = 30 ; c = 60 ; 11 = O ; 12 = 0 ; D = 1800.
Use this solution to determine the solution ofthe given primal model.
(10)
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Question 4 (17 marks)
Consider the following L-P model:
Minimize Q=2x+4y+5z+3t
Subject to -x-2y+2z
240
3x + 2z + t ::;100
X - 2y - Z + 4t 2 50
x;y;z;t 2 0
4.1 Re-write the model to include all the necessary variables.
(5}
4.2 Develop the first (not just the initial} tableau for the model and circle the pivot. DO NOT
SOLVE.
(12}
Question 5 (17 marks)
Consider the following transportation table:
Destination 1 Destination 2 Destination 3
Source 1
10
15
20
Source 2
12
7
9
Source 3
6
14
16
Demand
30
15
15
Supply
20
20
20
5.1 Determine the initial transportation cost using the North-west corner method. (6}
5.2 The following table is an estimate of the minimum cost of the transportation problem:
10
15
20
12
6
10
20
5
10
Use this table to determine the minimum cost for the transportation problem. (11}
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Question 6 (14 marks}
Given the following assignment table, assign workers A, B, C, and D to the tasks 1, 2, 3, and 4 in
such a way that assignment cost is at its minimum. Also calculate the minimum cost. (14)
Task 1
Task 2
Task 3
Task 4
Worker A 100
85
85
90
Worker B 45
95
65
75
Worker C 135
105
100
115
Worker D 55
120
105
125
END OF PAPER
TOTAL MARKS: 100
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