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Management Mathematics Ii (Day &Amp; Eve) Question Paper
Management Mathematics Ii (Day &Amp; Eve)
Course:Bachelor Of Commerce
Institution: Kca University question papers
Exam Year:2010
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UNIVERSITY EXAMINATIONS: 2009/2010
FIRST YEAR STAGE 2 EXAMINATION FOR THE DEGREE OF
BACHELOR OF COMMERCE
CMS 102: MANAGEMENT MATHEMATICS II (DAY & EVE)
DATE: APRIL 2010 TIME: 2 HOURS
INSTRUCTIONS: Answer Question ONE and Any other TWO Questions
QUESTION ONE
a) Outline the steps followed while determining the inverse of a 3X3 Matrix. (5 Marks )
b) State three characteristics of a transition matrix. (3 Marks )
c) Find the derivative of the implicit function below
2x5y2 – 4x1/2y1/4 = 2xy ( 5 Marks)
d) A food processing plant has a particular problem with the delivery and processing of perishable
goods with a short life. All deliveries must be processed in a single day and although there are a
number of processing machines available, they are very expensive to run. A researcher has
developed the function Y= 12x-2p-px2 to describe the profit (in sh”000”) . x is the number of
machines used and p is the number of deliveries in a day.
i) Show that the system is uneconomical if 4 deliveries are made in one day. (4 Marks)
ii) If three deliveries are made in one day, find the number of processing machines that should
be used in order to maximize the profit. What is the maximum profit in this case? (6 Marks)
e) A manufacturer knows that if x (in hundred) products are demanded in a particular week, the
average cost function(sh”000”) is 14/x + 3 and marginal revenue function(sh”000”) is 19 – 2x.
Required
i) Derive the total revenue, cost and profit functions (5 Marks)
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ii) Level of demand that will maximize profitability (2 Marks)
QUESTION TWO
ABC ltd has has two subsidiary companies; Kizuri and Bora. kizuri is solely involved in
manufacturing of ABC ltd’s products and Bora is the sole distributor of ABC’s products. Kizuri
operates as a cost centre and supplies all its products to Bora.The total cost of production for kizuri is
given by the equation C(k)=3q3-30q2+50q+300 where q is the number of units (in millions ) produced.
The total cost associated with Bora’s activities is given by
C(B)= 2q3 - 10q2+ 250q + 100. The revenue generated by Bora on selling q units is given by the
function R= 400q – 25q2
Required
a) The optimal number of units that Bora should receive from Kizuri so as to maximize its profit.
(7 Marks)
b) The optimal number of units that Kizuri should transfer to Bora (6 Marks)
c) The optimal number of units for ABC ltd as whole (7 Marks)
QUESTION THREE
a) Highlight the difference between input-output analysis and Markov analysis. (4 Marks)
b) Better comp and supercomp are two products produced by two competing companies; Todays
computer ltd and comptech ltd respectively.
Customers of the two companies are fairly brand loyal with Todays computer ltd and comptech
ltd retaining 80% and 70% of their customers respectively in each year.The current Market
share of Todays computer ltd is 50%.
Required
i) The Market share of each company in the next one year (5 Marks)
ii) The longrun Market share of each of the companies (8 Marks)
iii) Advise the management of the two companies based on your results in (b) (ii) above.
(3 Marks)
QUESTION FOUR
A firm’s total revenue is a function of the time taken (in minutes) of advertising in the
electronic media.The total revenue is given by the function: R= 90X + 150Y- 40XY-10X2-25Y2
Where: X is the time taken in advertising in the television per day
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Y is the time taken advertising on the radio per day.
Required
a) The total time of advertising in each medium that would maximize revenue. (7 Marks )
b) If the management restricts the total time of advertising in both media to 3 minutes per
day,how should the advertising time be shared between the two media in order to maximize
total revenue? (11 Marks)
c) The additional revenue if the advertising time in (b) above is increased by one minute.
(2 Marks)
QUESTION FIVE
A Miniature economy has three industries; Motor vehicles, Electricity and Steel.These industries are
interdependent such that the the output of one industry is the input of another.The following table
shows the input ratios of each industry.
Input
m/vehicles Electricity Steel
m/vehicles 0.17 0.25 0.25
Output Electricity 0.25 0.25 0.33
Steel 0.50 0.33 0.33
Required
a) Derive the Leontief’s inverse matrix (13 Marks)
b) Determine the primary inputs required by each industry if the final demand is sh216 million,
sh240 million and sh360million for motor vehicles, electricity and steel industries respectively.
(7 Marks)
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