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MFE512S - MATHEMATICS FOR ECONOMIS - 2ND OPP - JANUARY 2025 |
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-f
nAmlBIA UnlVERSITY
OF SCIEnCEAnDTECHnOLOGY
FacultoyfHealthN, atural
ResourceasndApplied
Sciences
Schoool f NaturalandApplied
Sciences
Departmentof Mathematics,
StatisticsandActuarialScience
13JacksonKaujeuaStreet
Private Bag13388
Windhoek
NAMIBIA
T: •264 612072913
E: msas@nust.na
W: www.nust.na
QUALIFICATION: BACHELOR OF ECONOMICS
QUALIFICATION CODE: 07BECO
LEVEL:5
COURSE:MATHEMATICS FOR ECONOMICS lB
COURSECODE: MFES12S
DATE: JANUARY 2025
SESSION: 2
DURATION: 3 HOURS
MARKS: 100
SECONDOPPORTUNITY/SUPPLEMENTAREYX: AMINATIONQUESTIONPAPER
EXAMINER:
MODERATOR:
Mrs. Yvonne Nkalle, Mrs. Lutopu Khoo & Mr. Tobias Kaenandunge
Mr. f/enikemanya Ndadi
INSTRUCTIONS:
1. Answer all questions on the separate answer sheet.
2. Pleasewrite 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.
PERMISSIBLE MATERIALS:
1. Non-Programmable Calculator
This paper consists of 3 pages including this front page
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Question 1 [ 7 Marks]
Solve the following system of linear equations, using matrix inversion method.
4x + 3y = 7
2x + y = 3.
Question 2 [3; 4; 3 Marks]
A company has five retail stores. Stores 1, there are 18 TV's (t), 23 camcorders (c) and 14
printers (p). Stores 2, there are 15 TV's (t), 20 camcorders (c) and 19 printers (p). Stores 3,
there are 18 TV's (t), 12 camcorders (c) and 24 printers (p). Stores 4, there are 10 TV's (t), 22
camcorders (c) and 11 printers (p). Stores 5, there are 13 TV's (t), 20 camcorders (c) and 18
printers (p). The price of one TV IS N$2300. One camcorder costs N$6024 and a printer costs
N$1050.
(a) Express this inventory in the matrix form.
(b) What is the total value is the stock in store 2?
(c) What is the value of all the printers in the five stores?
Question 3 [10 Marks]
Given A=[=~
[i i !]&B =
=~
5 -3 -1
21
Question 4 [11 Marks]
_\\], Find BA.
3
Solve the following system of linear equations, using Cramer's rule.
= + 2x1 x2 5
= + 3x1 - 2x 2 4x 3 8
Question 5 [11 Marks]
Solve the following system of linear equations, by Gaussian elimination Method.
9a + 3b + c = 64
36a + 6b + c = 133
81a + 9b + c = 208
Mathematics for Economics 1B (MFE512S)
1srOpportunity- November 2024 2
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Question 6 [S Marks]
Solve the following inequality 6(y - 3) 42.
Question 7 [7 Marks]
A small firm builds two types of garden shed. Type A requires 2 hours of machine time and 5
hours of craftsman time. Type B requires 3 hours of machine time and 5 hours of craftsman
time. Each day there are 30 hours of machine time available and 60 hours of craftsman. The
profit on each type A shed is N$60 and on each Type, B is N$ 84. Formulate the linear
programming model.
Question 8 [20 Marks]
Provide the solution to the following standard minimization problem, including all the steps.
Minimize C=20000 x1 + 25000x 2
Subject to:
400x 1 + 300x 2 :2::25000
300x 1 + 400x 2 :2::27000
200x 1 + 500x 2 :2::30000
Question 9 [9 Marks]
Find the Jacobian determinants of the following functions and evaluate it at (0, -2).
Conclude your answer.
f(x,y) = exy + y
g(x,y) = y2x
Question 10 [10 Marks]
Calculate the Hessian determinant at the following point (1,1), given the following function
and interpret your answers.
= f(x, y) eylnx,
Mathematics for Economics 1B (MFE512S)
1srOpportunity- November 2024 3