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Management Mathematics I Question Paper
Management Mathematics I
Course:Diploma In Business Management
Institution: Kca University question papers
Exam Year:2010
UNIVERSITY EXAMINATIONS: 2009/2010
STAGE II EXAMINATION FOR DIPLOMA IN BUSINESS MANAGEMENT
DMS 101: MANAGEMENT MATHEMATICS I
DATE: APRIL 2010 TIME: 1½ HOURS
INSTRUCTIONS: Answer any THREE questions
Question One
(a) Suppose that an amount of money P0 is invested in a saving account at interest rate k,
compounded continuously. The accrued amount P(t), after t years, is given by the exponential
growth model
P (t) = P0ekt.
(i) Suppose that Sh.25, 000 is invested and grows to Sh.45, 800.25 in 6 years. Find the
exponential growth function. [5 Marks]
(ii) How long will it take for the original amount to triple? [5 Marks]
(b) A newly created state welfare agency is attempting to determine the number of analysts to hire to
process welfare applications. Efficiency experts estimate that the average cost C (Sh.’00’) of
processing an application is a function of the number of analysts x. Specifically, the cost function
is
C = f(x) = 0.001 x2 – 5 ln x + 60
Given this logarithmic function:
(i) Determine the average cost per application if 20 analysts are used. [2 Marks]
(ii) Determine the average cost if 50 analysts are used. [2 Marks]
(iii) Draw the graph of the function for the domain of x from 10 to 100, taking steps of 10
units. [6 Marks]
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Question Two
a) Define the following terms as used in financial mathematics
(i) Principle [2 Marks]
(ii) Interest [2 Marks]
(iii) Rate of interest [2 Marks]
(iv) Accrued amount [2 Marks]
b) George invested Sh.75, 000 in a financial institution that pays compound interest. The rate of
interest payable per annum is 18% p.a. Find the number of years it takes for this amount to accrue
to Sh.238, 910.5425. [3 Marks]
c) After Sh.50, 000 has been invested in a Bank that pays compound interest; the accrued amount
after 6 years is Sh.149, 299.20. Find the rate of interest payable per annum. [3 Marks]
d) The net cash flows on a project are estimate to be as follows:
Year : 0 1 2 3 4 5
Net cash flow (Sh) : (25, 000) 8, 000 12, 000 9, 000 7, 000 7, 500
Required:
Using the NPV criterion and a discount rate of 14%, calculate the net present value of the
investment. [6 Marks]
Question Three
a) Define the following terms as used in set theory and illustrate with an example.
(i) Universal set
(ii) Equality of sets
(iii) Null set
(iv) Union set
(v) The set of intersection [10 Marks]
b) The main daily newspapers in Yairobi are: The National, The new Era and the Citizen. The
management of one of the dailies is concerned about the low sales volume of their paper. In a
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recent survey of 100 families in Yairobi, the numbers that read the various newspapers were found
to be as follows:
Newspaper Number of readers
The Citizen 28
Citizen and New Era 8
The New Era 30
Citizen and National 10
The National 42
New Era and National 5
All the three newspapers 3
Required:
(i) Determine the number of families who did not read any of the three newspapers.
[3 Marks]
(ii) Mrembo Beauty advertising firm in Yairobi wants to know which newspaper they
should advertise in so that they can reach the largest audience. Advise the
Company. [2 Marks]
c) Mr. Benjamin wishes to buy a car after 5 years. He decides to save Ksh.10, 000 every month and
deposits it into an account paying interest at 12% per annum.
Required:
The amount Benjamin would have to add to his saving after 5 years in order to be able to buy the
car if the cost of the car he wishes to buy after 5 years will be Ksh.1, 500,000. [5 Marks]
Question Four
a) What are the assumptions behind break-even analysis? [5 Marks]
b) A restaurant serves meals at an average price of £12. The variable cost of each meal is £8 and the
fixed costs of running the restaurant amount to £400 per day.
(i) If the restaurant sold 150 meals per day, what daily profit would the restaurant make?
[4 Marks]
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(ii) How many meals should the restaurant aim to serve each day in order to break even?
[3 Marks]
(iii) If the restaurant were making a loss of £200 per day, what increase in the number of meals
served would be required to break even? [3 Marks]
c) Two points (p, q) on a linear demand function are (Sh20, 80000) and (Sh30, 62500).
(i) Determine the demand function q = f (p).
(ii) What price would result in demand of 50000 units? [5 Marks]
Question Five
(a) Market surveys of suppliers of a particular product have resulted in the conclusion that the
supply function is approximately quadratic in form. Suppliers were asked what quantities
they would be willing to supply at different market prices. Results of the survey indicated
that at market prices of Sh.25, Sh.30 and Sh.40 the quantities which suppliers would be
willing to offer to the market were 112.5, 250.0 and 600.0 (thousand) units, respectively.
Required:
i) Determine the supply function [10 Marks]
ii) Determine the quantity supplied when the price is Sh.50 [2 Marks]
(b) It costs Thomas Sh.26, 000 to make 12 pairs of trousers and 8 shirts. The cost of 5 pairs of
trousers and 11 shirts is Sh.18, 500. Thomas makes a profit of 20% for each pair of trousers
made and sold and 30% on each shirt made and sold.
Required:
(i) The cost of making a pair of trousers and a shirt [4 Marks]
(ii) The selling price of a pair of trousers and a shirt [4 Marks]
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