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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:2009
1
UNIVERSITY EXAMINATIONS: 2008/2009
FIRST YEAR STAGE II EXAMINATION FOR THE DEGREE OF
BACHELOR OF COMMERCE
CMS 102: MANAGEMENT MATHEMATICS II
DATE: APRIL 2009 TIME: 2 HOURS
INSTRUCTIONS: Answer question ONE and any other TWO questions
QUESTION ONE
a) Differentiate between a diagonal matrix and a sub matrix (4 Marks)
b) Find the inverse of the matrix below;
3 1 2
A = 2 5 4
6 7 1 (6 Marks)
c) Find the derivative of the implicit function x3 + 3y4 – y2 – 4x = 0 (3 Marks)
d) The revenue in selling q units of a given product is given by the function
R= 480q – 6q2. Determine the number of units to be sold in order to maximize the revenue and
state the maximum revenue. (4 Marks)
e) The marginal revenue and marginal cost functions of a product are given by M.R=20-8x and
M.C= 2x2 – x + 5 respectively where x is the monthly output in thousands of tones. M.R and
M.C are in million shillings. Fixed costs amount to sh.100,000 per month.
2
Required
i) Derive the total revenue, total cost and total profit functions (8 Marks)
ii) Quantity that will maximize profit (3 Marks)
iii) The maximum profit (2 Marks)
QUESTION TWO
Nzewani Electronic Ltd. manufactures and sells a brand of television sets called LD – TVs. The three
closest competitor brands in the Market are SUM-TVs, SON-TVs and PAL – TVs. Because of the
custom manufacturing process and their inherent high costs, no other competitor has any effect on the
current Market. The year 2002 was an exceptionally good year in terms of gain-loss trade offs. The
year’s activity is summarized in the following table:
Brand
Number of customers
January 2002
Gain
Loss
Number of customer
December 2002
LD-TV 2,200 500 450 2,250
SUM-TV 3,000 600 700 2,900
SON-TV 2,300 250 250 2,300
PAL-TV 2,500 400 350 2,550
Further analysis resulted in the losses summary as follows:
Brand Number of customers
Losses to
LD-TV SUMTV
SON-TV PALTV
LD-TV _ 200 100 150
SUM-TV 400 _ 50 250
SON-TV 0 250 _ 0
PAL-TV 100 150 100 _
The Market shares for LD-TV, SUM-TV, SON-TV and PAL-TV in January 2002 were 22, 30, 23
and 25 per cent respectively.
3
Required:
a) Advise the management of Nzewani Electronic Ltd on the expected Market share for each brand at
the end of December 2002. (4 Marks)
b) Assuming the same pattern of switching persists, what would be the long run Market share for
each brand? (11 Marks)
c) What are the assumptions of the technique you have used in (a) and (b) above? (5 Marks)
QUESTION THREE
An Ujumi industry ltd has two subsidiary companies; Apex and maxima. Apex is solely involved in
manufacturing of ujumi’s products and maxima is the sole distributor of ujumi’s products. Apex
operates as a cost centre and supplies all its products to maxima. The total cost of production for Apex
is given by the equation CA=3q3-30q2+50q+300 where q is the number of units (in millions)
produced.
The total cost associated with maxima’s activities is given by
C M= 2q3 - 10q2+ 250q + 100. The revenue generated by maxima on selling q units is given by the
function R= 400q – 25q2
Required
a) The optimal number of units that maxima should receive from Apex so as to maximize its
profit. (7 Marks)
b) The optimal number of units that Apex should transfer to maxima (6 Marks)
c) The optimal number of units for ujumi ltd as whole (7 Marks)
QUESTION FOUR
a) Differentiate between definite and indefinite integration (4 Marks)
b) ABC Ltd is planning for an advertising and promotional campaign for its products. The
advertising and promotional campaign cost will be incurred at the rate C’ = k£ 10,880 per
day. Marketing specialists estimate that the rate at which revenue will be generated from the
promotional campaign can be estimated by the function R’ = 16,000-80t2 where t represents
the days of the campaign and R’ is measured in k£ per day.
Required
i) Sketch the functions C’ = 10,880 and R’ = 16,000-80t2 on the same axis. (4 Marks)
ii) How long the campaign should be conducted? (3 Marks)
4
iii) Compute the expected total costs of the advertising and promotional campaign
(3 Marks)
iv) Compute the expected total revenue from the advertising and promotional campaign
(3 Marks)
v) Compute the expected net profit from the advertising and promotional campaign
(3 Marks)
QUESTION FIVE
a) Define the following terms as used in input-output analysis:
i) Transactional table (2 Marks)
ii) Intermediate demand (2 Marks)
iii) Primary inputs (2 Marks)
iv) Technical coefficients (2 Marks)
b) Agricultural Ltd. has two inter-related industries in the Western region; Dairy and Vegetable
farming. The final demand for the outputs of Dairy and Vegetable farming are Sh.4,950 and
Sh.8,250 respectively. Out of one shilling produced by Dairy farming Sh.1/6 is for its own use
and Sh.1/3 is used by vegetable farming. On the other hand Vegetable sector uses Sh.1/4
while Sh.1/2 is used by the Dairy sector from one shilling it produces.
Required:
i) Determine for Agricultural Ltd. the output for each of the two industries or sectors to
satisfy demand for its products. (6 Marks)
ii) Account for the usage of the two sectors’ output (6 Marks)
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