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MFE512S - MATHEMATICS FOR ECONOMISTS - 2ND OPP - JAN 2023 |
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nAmlBIA UnlVERSITY
OF SCIEnCE Ano TECHnOLOGY
FACULTY OF HEALTH AND APPLIED SCIENCES
DEPARTMENT OF MATHEMATICS AND STATISTICS
QUALIFICATION:BACHELOROF ECONOMICS
QUALIFICATIONCODE: 07BECO
COURSECODE: MFE512S
SESSION:JANUARY 2023
DURATION: 3 HOURS
LEVEL: 5
COURSENAME: MATHEMATICS FOR
ECONOMISTS 1B
PAPER:THEORY
MARKS: 100
SUPPLEMENTARY /SECOND OPPORTUNITY EXAMINATION QUESTION PAPER
EXAMINER
Mr. T. KAENANDUNGE, Mr. F. Ndinodiva, MS Y. NKALLE
MODERATOR:
Mr. I.D.O. NDADI
INSTRUCTIONS
1. Answer ALL the 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.
PERMISSIBLE MATERIALS
1. Non-programmable calculator without a cover.
ATTACHMENT: Graph paper
THIS QUESTION PAPERCONSISTSOF 3 PAGES(Including this front page)
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MFE512S- MATHEMATICS FOR ECONOMISTS 1B: 2NoOPPORTUNITY/SUPPREMENTARY
EXAMINATION QUESTION PAPER-JANUARY, 2023
QUESTION 1
[33]
2
2
1.1 lfA=[l
],B=[-
-SJ,evaluate(ABf1withoutworkingouttheproductAB.
[10J
34
8 -9
1.2
Find the exact value(s) of x which make matrix M = [:
! !2] x
singular.
[6J
7 8 x+5
1.3 The Ace Novelty company received an order from the Magic World Amusement Park for
1200 "Pink Panthers", 1800 "Giant Pandas" and 1400 "Big birds". The quantity of each type
of stuffed animal to be produced at each plant is shown in the production matrix
P.Panthers G.Pandas B.Birds
p _ L.A. [700
Seattle 500
1000
800]
800
600
Each Pink Panther requires 1.3 square yards of plush, 20 cubic feet of stuffing material and 12
pieces of trimming; each Giant Panda requires 1.5 square yards of plush, 30 cubic feet of
stuffing material, and 5 pieces of trimming; each Big Bird requires 2.5 square yards of plush,
25 cubic feet of stuffing material, and 15 pieces of trimming. The plush costs $4.50 per square
yard, the stuffing material costs $0.10 per cubic foot, and the trimming costs $0.25 per unit.
Represent the given information in matrices and use matrix operations to answer the
following questions.
1.3.1
Find the amount of each type of material to be purchased for each of the two plants.
1.3.2
1.3.3
[10J
Find the total cost of materials to be incurred at each plant.
[SJ
Find the total cost of materials incurred by Ace Novelty Company in fulfilling the order.
[2J
Question 2
[29]
2.1 A cashier has 15 coins consisting of N$1s, N$Ss,and SOcswith a value of N$41-00. If the
number of N$Ss is 1 less than twice the number of N$1s, how many of each type of coin
does she have? Use Gaussian elimination.
[11J
2.2
2.2.1
A motor company manufacture and sell cars and motorbikes. The cost of manufacturing x
motorbikes and y cars is given by C(x,y) = 800x2 +400.xy + 2900y2. Each motorbike is
sold for N$36 000-00 and each car is sold for N$180 000-00.
Use Gaussian elimination to determine the number of motorbikes and the number of cars
that should be manufactured and sold for a maximum profit P and determine the
maximum profit pmax.
[8J
2.2.2 Use the Hessian to confirm that the amounts in 2.2.1 will produce maximum profit.
[SJ
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MFE512S-MATHEMATICFSORECONOMISTSlB: 2NDOPPORTUNITY/SUPPREMENTARY
EXAMINATIONQUESTIONPAPER-JANUARY2,023
2.2.3 Use the Jacobian to test for functional dependence between the cost function and the
revenue function.
[5]
Question 3
[38]
3.1 Malu plans to invest no more than N$20,000 in two different interest-bearing accounts. Each
account is to contain at least N$5000. Moreover, one account should have at least twice the
amount that is in the other account. Find a system of inequalities describing the various
amounts that can be deposited in each account, and sketch the graph of the system. (Make
a sketch on your answer sheet. Do not use the graph paper.)
[10]
3.2 CassyFinance Company has a total of N$20 million earmarked for home loans and
automobile loans. On the average, home loans will have a 10% rate of return on the loans
given out while automobile loans will yield a 12% rate of return on the loans extended.
Management has also stipulated that the total amount of home loans should be atleast four
times the total amount of automobile loans. Use the graphical method to determine the
total amount of loans the company should extend to each of the two categories of
customers in order to maximise the rate of return on the loans extended.
[10]
3.3 A company has budgeted a maximum of N$600,000 for advertising a certain product
nationally. Each minute of television time costs N$60,000 and each one-page newspaper
advertisement costs N$15,000. Eachtelevision advertisement is expected to be viewed by
15 million viewers, and each newspaper advertisement is expected to be seen by 3 million
readers. The company's market research department advises the company to spend at most
90% of the advertising budget on television advertisements. How should the advertising
budget be allocated to maximize the total audience? Use the simplex method.
[10]
3.4 Use the dual method to solve the following minimization problem.
Minimise C = 4x + 2y + 6z
Subject to x + 2y + z ;:::4
2x+ y+2z;::: 2
[8]
3x+2y+z;:::3
x,y,z ;:::o
****************************END OFEXAMINATION***************************
GOODLUCK!!!!!!!!!
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