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Cms 102 Management Maths Ii Question Paper
Cms 102 Management Maths Ii
Course:Bachelor Of Commerce
Institution: Kca University question papers
Exam Year:2012
1
UNIVERSITY EXAMINATIONS: 2011/2012
YEAR I EXAMINATION FOR THE BACHELOR OF COMMERCE
CMS 102 MANAGEMENT MATHS II
(SUNDAY)
DATE: APRIL 2012 TIME: 2 HOURS
INSTRUCTIONS: Answer Question One and Any other Two Questions
QUESTION ONE
a) Differentiate between the following terms;-
i. Open input output model and closed input-output model [2 Marks]
ii. Marginal revenue and marginal cost [2 Marks]
b) Show that
? ? ?
?
?
? ? ?
?
?
=
1 1 0
1 0 1
0 1 1
A satisfies the equation A3 - 3A - 2I = 0 hence find A-1 . [7 Marks]
c) A university’s service department is considering leasing one of two possible computers. A
computer can be found in operating condition (O) or nonoperating condition (NO). The daily
transition matrix of the two computers under identical maintainance follows:
Computer A Computer B
O NO O NO
O 0.95 0.05 O 0.98 0.02
NO 0.90 0.10 NO 0.85 0.15
Which computer should the university lease if the leasing charges are the same? [6 Marks]
d) A factory produces x calculators per day. The total daily cost in shillings incurred is
5x2 - 800x + 500. if the calculators are sold for Sh. (100 -10x) each, find the number of
2
calculators that would maximize the daily profit. [5 Marks]
e) Digital Ltd manufactures and sells floppy disks at Nairobi Industrial area. The Average Total
Cost (ATC) and Average Revenue (AR) in thousands of shillings of producing x floppy disks
are given by the following functions
x 2 x 50 500 x
5
2
ATC = 1 2 - + + and AR = 800 - 2x2 where x is the number of floppy disks
produced. Determine :-
i. The profit function [3 Marks]
ii. The number of floppy disks required to maximize profit [3 Marks]
iii. The maximum profit [2 Marks]
QUESTION TWO
The following table indicates the customers buying behaviour for a given product Produced by ABC
Company with two brands. Currently, the market share for Brand A is 27.5%, Brand B is 37.5% and
Competitor’s Brand C is 35%.
Next months brand
Choice
Current months
Choice
Brand A
Brand B
Competitors
Brand C
Brand A
Brand B
Competitors Brand C
0.2
0.1
0.5
0.2
0.5
0.2
0.6
0.4
0.3
Determine:
a) The market shares one month from now. [2 Marks]
b) The long run probabilities [3 Marks]
c) ABC Company is considering two alternative policies for promoting its products
3
1. Promote Brand A only. This will cost Sh. 150,000 invested in a lump sum and is expected
to change the transition matrix to:
To
From
A B C
A 0.6 0.2 0.2
B 0.4 0.4 0.2
C 0.6 0.1 0.3
2. Promote Brand B only. This will cost Sh. 280,000 invested in a lump sum and is expected
to change the transition matrix to:
To
From
A B C
A 0.1 0.5 0.4
B 0.2 0.8 0
C 0.3 0.5 0.2
Required:
i. Which policy will bring larger increases in ABC’s total share of the market in the long run?
[9 Marks]
ii. Which policy will be more efficient in terms of the gain per one thousand shilling invested in
the long run? [3 Marks]
iii. Assume that each percentage of increased share in the total market is worth Sh.10,000 to
ABC’s; which policy (if any) should ABC take? [3 Marks]
QUESTION THREE
a) Evaluate the following integrals
i. dx
? x 5 +17
1 [3 Marks]
4
ii. ? x l xdx 2 [3 Marks]
iii. dx
x x
x ? +
+
3 2
12 2 [3 Marks]
iv. ? ?
-
+
3
1
2
1
(x y)dydx [3 Marks]
b) A non-governmental organization is conducting its annual fund-raising campaign for its summer
camp program for the disadvantaged. Campaign expenditures will be incurred at a rate of Sh.10,
000 per day. From past experience it is known that contribution will be high during the early
stages of the campaign and will tend to fall off as the campaign continues. The function
describing the rate at which contribution are received is C(t) = -100t 2 + 20000 where t
represents the day of the campaign, and C(t) equals the rate at which contributions are received,
measured in shillings per day. The organization wishes to maximize the net proceeds from the
campaign.
i. Determine how long the campaign should be conducted in order to maximize net proceeds.
[2 Marks]
ii. What is the total campaign expenditures expected to equal? [2 Marks]
iii. What are the total contributions expected to equal? [2 Marks]
iv. What are the net proceeds (total contribution less total expenditures) expected to equal.
[2 Marks]
QUESTION FOUR
a) A bus company uses the function P(x) (3 0.6x) 2 0.1x
1 = + - to estimate the net weekly profit in
thousands of shillings, if a particular bus route is x miles long.
i. How long should the route be to maximize the net profit? [5 Marks]
ii. What would be the value of the maximum net profit? [3 Marks]
b) An economy consists of three industries X, Y and Z and each produces one product. The
interaction of the use of X, Y and Z production over some fixed period of time is as shown
below:
5
X Y Z Final
demand
Total
Production
X
Y
Z
100
40
60
40
60
40
80
40
40
140
180
100
360
320
240
Suppose demand is expected to increase by 30% for X and Y and reduce by the same percentage
for Z industries. What must the total output be to meet this projected demand?
[12 Marks]
QUESTION FIVE
a) Determine the first derivatives of the following functions;
i. y = x 2x + 3 [2 Marks]
ii. 5 3 4 f (x) = 10l x - [2 Marks]
iii. f (x) = ln(5x2 - 2x +1) [2 Marks]
b) An automobile manufacturer estimates that the annual rate of expenditure r(t) for maintenance
on one of its model is represented by the function r(t) = 100 +10t 2 .
i. What is the expected maintenance expenditures during the automobile first 10 years? [3 Marks]
ii. Of the above expenditures, what is expected to be incurred during the tenth year? [2 Marks]
c) A company manufacturing three products X, Y and Z, each of which must go through three
processes A, B and C for the following times:
Product
Time spent in the process
A B C
X
Y
Z
2
1
2
5
2
2
1
3
3
The maximum capacities of processes A, B and C are 1100, 1800 and 1400 respectively. Using
the matrix method, calculate the number of units to be produced of products X, Y and Z to ensure
the utilization of maximum capacity? [9 Marks]v
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