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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 - SUNDAY
DATE: AUGUST 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) Transpose of a matrix ( 2 marks)
ii) Identity matrix ( 2marks)
iii) Null matrix ( 2marks)
b) Evaluate the integral below
?2(2x +4)5dx (4marks)
c) The Average revenue of company is given by the expression A.R= 20q – q2 while its
marginal cost is given by the expression M.C= 4q-10. Fixed costs amount to sh25 and q
represents the number of units produced and sold by the company.
i) Derive the total revenue, total cost and total profit functions (7marks)
ii) Quantity that will maximize profit (3marks)
iii) The maximum profit (2marks)
d) A firm’s annual profit is stated as a function of the number of sales persons employed. The
profit function is given by p =40xe-0.002x where p is the profit in thousand of shillings and x is
the number of sales persons.
2
Required
i) Determine the number of sales persons which will maximize the annual profit.
( 6 marks )
ii) Compute the maximum profit expected. ( 2 marks )
QUESTION TWO
A manufacturer uses machine Z in one of its production processes. Due to its constant usage, the
machine is inspected for maintenance purposes on a monthly basis. On inspection, the condition of the
machine is classified into four possible states as follows:
State 1: Good
State 2: Minor repairs
State 3 : Major repairs
State 4: Write off.
Thereafter the manufacturer adopts either of the following maintenance policies:
Policy 1: Minor repairs if the machine is in state 2, overhaul if the machine is in state 3 and replace if
the machine is in state 4.
Policy 2: Minor repairs if the machine state 1, 2 0r 3 and replace the machine if it is in state 4.
The costs of maintenance associated with each policy are shown in the table below:
State Policy 1 Policy 2
Sh Sh
1 0 0
2 100,000 100,000
3 400,000 300,000
4 600,000 600,000
The transition probability matrices for each policy are as given below:
Policy 1 Policy 2
1 2 3 4 1 2 3 4
1 0 0.8 0.1 0.1 1 0 0.8 0.1 0.1
2 0.1 0.6 0.2 0.1 2 0 0.5 0.4 0.1
3 0.05 0.3 0.45 0.2 3 0 0 0.4 0.6
4 1 0 0 0 4 1 0 0 0
3
Required
a) The longrun proportion of times the machine would be expected to be in each state if policy 1
is adopted. ( 8 marks )
b) The longrun proportion of times the machine would be expected to be in each state if policy 2
is adopted. ( 8 marks )
c) The expected longrun average cost for each policy. ( 4 marks )
QUESTION THREE
a) Two students were discussing about the relationship between average cost and total cost. One
student said that since average cost is obtained by dividing the cost function by the number of
units Q, it follows that the derivative of the average cost is the same as marginal cost, since the
derivative of Q is 1
Required:
Comment on this analysis. (4 marks)
b) Gatheru and Kabiru Certified Public Accountants have recently started to give business
advice to their clients. Acting as consultants, they estimated the demand curve of a client’s
firm to be:
AR = 200 – 8Q
Where AR is average revenue in millions of shillings and Q is the output in units.
Investigations of the client firm’s cost profile shows that marginal cost (MC) is given by:
MC = Q² – 28Q + 211 (in millions of shillings)
Further investigations have shown that the firm’s cost when not producing output is Sh.10
million.
Required:
i) The equation of total cost (5 marks)
ii) The equation of total revenue (2 marks)
iii) An expression for profit (2 marks)
iv) The level of output that maximizes profit (5 marks)
v) The equation of marginal revenue (2 marks)
4
QUESTION FOUR
a) Differentiate between Differentiation and Integration (4 marks)
b) ABC Ltd manufactures and sells two interdependent products, namely, Super and Excel. The
demand functions for the products are given by:
P1 = 800 – x - 2y and P2 = 1100 – x - 2.5y where P1 is the unit price of Super and P2 is the unit
price of Excel. X and y are the number of units sold for Super and Excel respectively. The total
cost of producing both products is given by the function TC = 150x + 50y.
Required
i) The total revenue function (3marks)
ii) The total profit Function (3marks)
iii) The number of units of each product required to maximize total profit (6 marks)
iv) The maximum profit ( 4marks)
QUESTION FIVE
a) National exporters (NE) Ltd manufactures Agricultural, Industrial and mineral products. One
shilling worth of Agricultural output requires inputs worth sh0.1,sh0.15 and sh0.20 from
Agricultural, Industrial and mineral products respectively. One shilling worth of Industrial
output requires inputs worth sh0.25,sh0.15 and sh0.30 from Agricultural, Industrial and
mineral products respectively. One shilling worth of Mineral output requires inputs worth
sh0.24,sh0.16 and sh0.16 from Agricultural, Industrial and mineral products respectively.
In the next financial year, NE Ltd Plans to produce products worth Sh 40 million, Sh 20
million and Sh 50 million for the Agricultural, Industrial and mineral products respectively.
Required
i) Derive the technological matrix ( 3 marks )
ii) Write down the intermediate demand for each type of product ( 6 marks )
iii) Compute the final demand for each type of product. (3 marks )
iv) Compute the total worth of primary inputs ( 4 marks )
b) State the assumptions of the technique you have used to solve part (a) above ( 4 marks )
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