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MFE512S - MATHEMATICS FOR ECONOMIS - 1ST OPP - NOVEMBER 2024 |
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nAml BIA UnlVERSITY
OF SCIEnCE AnDTECHnOLOGY
FacultoyfHealthN, atural
ResourcaensdApplied
Sciences
Schoool f NaturalandApplied
Sciences
Departmentof Mathematics,
StatisticsandActuarialScience
13JacksonKaujeuaStreet
PrivateBag13388
Windhoek
NAMIBIA
T: +264612072913
E: msas@nust.na
W: www.nust.na
QUALIFICATION: BACHELOR OF ECONOMICS
QUALIFICATIONCODE: 07BECO
COURSE:MATHEMATICS FOR ECONOMICS lB
LEVEL:5
COURSECODE: MFES12S
DATE: NOVEMBER 2024
DURATION: 3 HOURS
SESSION: 1
MARKS: 100
EXAMINER:
MODERATOR:
FIRST OPPORTUNITY: EXAMINATION QUESTION PAPER
Mrs. Yvonne Nkalle, Mrs. Lutopu Khoo & Mr. Tobias Kaenandunge
Mr. llenikemanya Ndadi
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.
PERMISSIBLE MATERIALS:
1. Non-Programmable Calculator
This paper consists of 3 pages including this front page
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Question 1 [10 Marks]
Given the matrix A = [~ ~], find "k" and "h", so that A2 + kl = hA.
Question 2 [10 Marks]
-4 4
1 Given A= ~7 1
-3
Question 3 [ 7 Marks]
Solve the following system of linear equations, using matrix inversion method.
Sx + 2y = 3
3x + 2y = 5.
Question 4 [11 Marks]
Solve the following system of linear equations, using Cramer's rule.
x-y=3
2x + 3y + 4z = 17
y+ 2z = 7
Question 5 [11 Marks]
Solve the following system of linear equations, by Gaussian elimination Method.
4x + 3y + 6z = 25
x - 13 + Sy + 7z = 0
2x + 9y + z = 1
Question 6 [5 Marks]
Solve the following inequality -3 < 4x + 1 :5 17.
Question 7 [7 Marks]
Suppose a manufacturer of printed circuits has a stock of 200 resistors, 120 transistors and
150 capacitors and is required to produce two types of circuits. Type A requires 20 resistors,
10 transistors and 10 capacitors. Type B requires 10 resistors, 20 transistors and 30
capacitors. If the profit on that type A circuits is N$5 and that on type B circuits is N$12.
Formulate a linear programming model.
Mathematics for Economics 1B (MFE5125)
1srOpportunity- November 2024 2
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Question 8 [9 Marks]
Find the Jacobian determinants of the following functions and evaluate it at {1,2). Conclude
your answer.
f(x, y) = x4 + 3y2x
g(x,y) = Sy2 - 2xy + 1
Question 9 [10 Marks]
Calculate the Hessian determinant at the following point {1,1), given the following function
and interpret your answers.
f(x, y) = x2y + y 2x
Question 10 [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
300x 1 + 400x 2
200x 1 + 500x 2
25000
27000
30000
Mathematics for Economics 1B (MFE512S)
1srOpportunity- November 2024 3