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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
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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 & EVENING CLASS)
DATE: DECEMBER 2009 TIME: 2 HOURS
INSTRUCTIONS: Answer Question ONE and Any other TWO Questions
QUESTION ONE
a) Define the following terms as used in matrices
i) Symmetric matrix ( 2 Marks)
ii) Scalar matrix ( 2 Marks)
iii) Sub-matrix ( 2 Marks)
b) Find the derivative of the function below
Y= (5x4 + 8x2 – 20)5
(4 Marks)
c) The Marginal revenue of a company is given by the expression M.R= 40q – 3q2 while its
average cost is given by the expression A.C= 2q -10 + 50/q. q represents the number of units
produced and sold by the company.
i) Derive the total revenue, total cost and total profit functions (5 Marks)
ii) Quantity that will maximize profit (5 Marks)
iii) The maximum profit (2 Marks)
d) In year 2008, the head of the research and development department of ABC Ltd claimed that
the cost of producing solar panels would drop at the rate given by C’= -58/(3t + 2)2 where
0=t=10. C’ is in shillings per peak watt for the next t years.A peak watt is is the power
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produced at noon on a sunny day.t=0 corresponds to the beginning of year 2008.At the
beginning of year 2008, the panels which were used costed sh800 per peak watt.
Required
i) Find an expression giving the cost per peak watt of producing solar cell
Panels at the beginning of year t. (6 Marks)
ii) What will the cost per peak watt at the beginning of year 2018? (2 Marks)
QUESTION TWO
Angels of Mercy Mission Hospital operates on charity basis. The hospital’s board of directors has
recently complained about the increasing size of the cost budget insisting that the management should
cut down on costs.
The major concern of the board is the cost of maintaining patients at the intensive care unit (ICU).
The following information is available on the operations of the hospital:
1. The average cost of maintaining a patient at the ICU per week is Sh.200,000 compared to
Sh.100,000 per week incurred in maintaining a patient at the high dependency unit (HDU) and
Sh.50,000 per week of maintaining a patient at the general wad (GW)
2. Past information on patients indicates that:
(i) 50% of the patients in ICU at the beginning of the week will remain in ICU at the end
of the week and 50% will be transferred to HDU by the end of the week.
(ii) 10% of the patients in HDU at the beginning of the week will be transferred to ICU,
50% will remain in HDU, and 40% will be transferred to GW.
(iii) 85 % of the patients in the GW at the beginning of the week will remain in GW at the
end of the week, 10% will be transferred to HDU and 5% to ICU.
3. The board of directors believe that the criteria for maintaining patients in the ICU is too strict
and should be relaxed so that only 40% of the patients in ICU at the beginning of the week
remain there at the end of the week while 60% are transferred to HDU.
4. The staff at the hospital insist that if the proposed criterion is adopted.:
(i) 20% of patients in HDU at the beginning of the week will be transferred to ICU, 50%
will remain in HDU while only 30% will be transferred to GW.
(ii) No changes will be expected in the GW.
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5. Past hospital records indicate that the hospital serves an average of 4,000 patients weekly.
Required:
a) The steady state weekly costs under the current policy. (9 Marks)
b) The steady state weekly costs under the proposed policy. (9 Marks)
c) Advise the board on the best policy. (2 Marks)
QUESTION THREE
a) A miniature economy has three industries: motor vehicle, electricity and steel. These industries
are interdependent, such that, the outcome of one industry is the input of other. The following
table shows the input ratios of each industry.
m/vehicle Electricity Steel
Motor vehicles 0.17 0.25 0.25
Output Electricity 0.25 0.25 0.33
Steel 0.50 0.33 0.33
The Leontief inverse matrix is computed as below:
3.08 1.98 2.15
(I-A)-1= 2.64 3.41 2.70
3.96 3.19 4.46
Required
i) Define the term ‘input ratio’ (2 Marks)
ii) Interpret the input column and output row for motor vehicles using the input ratio table.
(6 Marks)
iii) Determine the primary inputs required by each industry if the final demand is sh 216
million, sh 240 million and sh 360 million for motor vehicles, electricity and steel
industries respectively. (8 Marks)
b) State four assumptions of input- output model. (4 Marks )
QUESTION FOUR
a) XYZ Company Limited invests in a particular project and it has been estimated that after X
months of running, the cumulative profit (Sh.’000’) from the project is given by the function
10X – X² - 5, where X represents time in months. The project can run for eleven months at
the most.
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Required:
i) Determine the initial cost of the project. (2 Marks)
ii) Calculate the break-even time in months for the project. (3 Marks)
iii) Determine the best time to end the project. (3 Marks)
iv) Determine the total profit within the break-even points. (4 Marks)
b) Maxim limited is an upcoming Manufacturing company at kariobangi. The company is planning
for an advertising and promotional campaign for its products. The advertising and promotional
campaign will be incurred at the rate of sh 9,000 per day. The rate at which the revenue will be
generated from the promotional campaign is estimated by the function R’= 17,000-80t2 where t
represents the days of the campaign and R’ is measured in ksh per day.
Required
i) How long should the campaign be conducted? (2 Marks)
ii) Compute the expected net profit from the advertising and promotional campaign.
(6 Marks)
QUESTION FIVE
Two competing products, A and B are manufactured by a monopolist. The profiles of the two products
are as follows:
Product A:
Selling price per unit=P1
Variable cost per unit= Sh 9
Demand function,q1= 2 P2 - 2P1 + 4
Product B:
Selling price per unit=P2
Variable cost per unit= Sh 12
Demand function,q
2= P
1/4 – 5/2 P2 + 52
Required
a) The joint revenue function for both products (4 Marks)
b) The joint cost function for both products (4 Marks)
c) The joint profit function (4 Marks)
d) Determine the prices and quantities of the output that would maximize the joint profit. (8 Marks)
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