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Cms 102 Management Mathematics Ii Question Paper
Cms 102 Management Mathematics Ii
Course:Bachelor Of Commerce
Institution: Kca University question papers
Exam Year:2011
1
UNIVERSITY EXAMINATIONS: 2010/2011
FIRST YEAR EXAMINATION FOR THE DEGREE OF BACHELOR OF
COMMERCE
CMS 102 MANAGEMENT MATHEMATICS II
DATE: DECEMBER2011 TIME: 2 HOURS
INSTRUCTIONS: Answer Question One and Any Other Two Questions
Question One
a) Define the following terms as used in matrices
i) A symmetric matrix ( 2 Marks)
ii) Identity matrix ( 2Marks)
iii) Determinant of a matrix ( 2Marks)
b) Find the inverse of the matrix below;
8 4 18
A = 10 8 16
12 12 14 (6Marks)
c) Determine the critical or turning point(s) of the function below:
2
750 5 3 5 2 500
2 2
Y= x- x+ x- (4Marks)
d) The Average revenue of a company’s product is given by the expression A.R= 20- q while
its marginal cost is given by the expression M.C= 4q-10. Fixed costs amount to sh20 and q
represents the number of units produced and sold by the company.
i) Derive the total revenue, total cost and total profit functions (9Marks)
ii) Quantity that will maximize profit (3Marks)
iii) The maximum profit (2Marks)
Question Two
Amalgamated Steel (AS) is one of the major producers of steel in the country. The sales of AS are
made to the industrial users rather than the consuming public. Through co-operative studies with
AS’s customers, the following technical coefficients matrix, in shillings was developed.
Steel Motor
Vehicles
Construction Metal
products
Iron Ore
Steel 0.20 0.25 0.15 0.30 0.10
Motor Vehicles 0.05 0.10 0.05 0.00 0.20
Construction 0.00 0.05 0.02 0.05 0.05
Metal products 0.10 0.05 0.05 0.05 0.10
Iron ore 0.25 0.00 0.00 0.00 0.00
The Leontief inverse matrix, (I-A)-1 is:
Required
a) Using the technical coefficients matrix, interpret the column and row for steel. (4 Marks)
1.4 0.4 0.3 0.5 0.3
0.2 1.2 0.1 0.1 0.3
0.1 0.1 1.0 0.1 0.1
0.2 0.1 0.1 1.1 0.2
0.4 0.1 0.1 0.1 1.1
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b) The columns in the technical coefficients matrix do not sum to one shilling. Why?
(2 Marks)
c) Determine the demand for steel, motor vehicles, construction, metal products and iron ore
if their autonomous demand is sh 2 million, sh 20 million, sh 15 million, sh 10 million, sh 1
million respectively. (5 Marks)
d) The Executive director of AS is interested in predicting the change in demand for steel
caused by increases of sh 5 million in motor vehicle sales, sh 3 million in construction and a
decrease of sh 2 million in sales of metal products. Determine the demand for steel, motor
vehicles, construction, metal products and iron ore upon these changes. (7 Marks)
e) What is the objective of the technique you have used to solve parts (c) and (d)? (2 Marks)
Question Three
In a recent research survey by intelligence consultants on the use of the services of auditing firms
by various non-governmental organizations (NGO’S) in Kenya, the findings were as follows.
Out of those NGO’S which used P& m Auditors in 2001 financial year, 10% switched to D&T
Auditors, 10% switched to best Auditors and 10% switched to Excel Auditors. Out of those which
used D& T auditors in the same, financial year, 20% switched to Best Auditors and 10% to excel
Auditors.
Out of those which were using best auditors, only 10% switched to Excel Auditors. Out of those
which used excel auditors, 20% switched to P& m Auditors, 10% to D &T Auditors and 10% to
best Auditors in 2002 financial year.
It was further found that year 2002 market share of p &m Auditors, D&T Auditors, Best Auditors
and Excel Auditors was 20%, 30%, 40% and 10% respectively.
Required
i) The matrix of transition probabilities (5 Marks)
ii) Year 2003 market share for each Audit form (6 Marks)
iii) The long run market share for each Audit firm (9 Marks)
Question Four
a) Differentiate between Differentiation and Integration (4 Marks)
b) Alpha industries sell two products, X and Y in related markets. Their demand functions are
as follows:
4
Px = 13-2x-y
Py = 13-x-2y
The total cost, in shillings is given by C = x + y
Determine the price and output for each good which will maximize profits (8Marks)
c) Explain the terms below as used in markov analysis:
i) Absorbing state (2 Marks)
ii) Closed state (2 Marks)
d) Outline the steps followed in determining the inverse of a 3 by 3 matrix. (4 Marks)
Question Five
Due to the expansion of business in Tanzania in recent years, Economical products ltd have set up
a marketing division in Tanzania responsible for selling a new product. The head office and
manufacturing plant still remain in Kenya. The company’s financial director has estimated that the
total cost of manufacturing in Kenya and the cost of transportation for the production can be given
by the function:
C = q2 + 20q + 40 where C is the total cost per week in thousands of shillings and q is the
quantity of the product sold.
This cost appears in the accounts for the manufacturing division. The total cost of the marketing
division in Tanzania is given by the function:
C = q2 + 140q + 200 which includes a transfer price of sh 100 per unit paid by the marketing
division to the manufacturing division. This cost appears in the accounts of the marketing division.
The revenue function for the marketing division has been estimated as: R = 500q – 8q2 where R is
the total revenue per week in thousand of shillings.
Required
a) Calculate the optimal policy for:
i) Marketing division (5 Marks)
ii) Manufacturing division (5 Marks)
iii) Company as a whole (5 Marks)
b) Compare the profit figures for each division and the company under the different policies
in (a) above. How does this type of situation affect the autonomy of the individual divisions
in the company? (5 Marks)
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