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Dms 111:Quantitative Methods For Business Question Paper
Dms 111:Quantitative Methods For Business
Course:Bachelor Of Commerce
Institution: University Of Nairobi question papers
Exam Year:2013
UNIVERSITY OF NAIROBI
FIRST SEMESTER EXAMINATION- 2012/2013
FIRST YEAR EXAMINATION FOR THE DEGREE OF BACHELOR OF COMMERCE
DMS 111: QUANTITATIVE METHODS FOR BUSINESS
DATE: JANUARY 23, 2013 TIME: 9.00AM-11.00AM
INSTRUCTIONS:
The paper contains four questions
Attempt question ONE and any other TWO questions: a total of THREE questions
Show all your working clearly
QUESTION ONE: COMPULSORY
for each of the following questions indicate whether it is TRUE or FALSE
The infinite set contains all the elements being analysed
“Set of all students in Lower Kabete Campus” is a well defined set.
The empty set is not a member of any set
Markov chains are stochastic processes
In set theory, (AUB)'=A'nB'
If the monthly sales of q items priced at sh. p per unit is given by q = -6p + 100, then the monthly sales decreased by 6 items for every sh.1 increase in price
A dependent variable s also called an explanatory variable
Cost of a product is given
In matrix algebra, a vector cannot be inverted (9marks)
The marginal cost of a product is given as:
MC = 6(q-2)2 shillings per unit where q=quantity produced.
Required:
The increase in total cost if level of production increase from 5 to 25 units. (4 marks)
An advertising company is interested in the retention rate of a person exposed to an advert t hours after the subject views the advert. In one such advert, subjects were asked to look at a picture which contained many different objects. At different intervals after this, they would be asked to recall as many objects as they could. Based on the experiment, the following function was developed:
R=95-20 ln t
Where R equals the average percentage recall and t equals time in hours since studyin the picture.
Required.
The recall percentage after 2 hours (1mark)
The rate of recall after 10 hours and interpret it. (2marks)
The time when the recall percentage is 40% (2marks)
The supply and demand functions for a product are given as follows:
Supply function: x - y +5 = 0
Demand function: (x+10)(y+5)=400
Where x represents price and y represents quantity.
Required:
The market equilibrium price and quantity. (4marks)
The input/output of technical coefficients matrix, A of an economy with 2 sectors, P and Q is:
A=Output ¦(P@Q) (¦( 0.5&0.2@0.1&0.2)¦ )
The final demands for the current planning period are estimated to be ksh. 50 billion and ksh.70 billion for the sectors p and q respectively
Required
The intermediate demands for each sector for the current planning period. (5 marks)
A survey of 825 consumers of mango (M) and apple (A) juices revealed that 425 preffered mango juice whereas 525 preffered apple juice.
Required:
The LEAST number of consumers who had preference for both juices (3 marks)
(Total 30 marks)
QUESTION TWO
Three firms in Puani County: Amina ltd (A), Bakari investments (B) and Chengo brothers (C), compete in the lucrative market for Korosho. Currently, their market shares are 50%, 20% and 30% for A, B and C respectively.A marketing consultant has found out the following concerning their competition from one year to another:
A losses 30% of its customers to B, but none to C.
B retains 70% of its customers and loses 30% to C
C loses 40% of its customers to A but none to B
Required
The transition matrix if the process is modeled as a markov process (4 marks)
The market shares foe each firm two years from now (4 marks)
The annual cost for the three firms rare estimated to be ksh. 1.3 million, ksh.1.4 million and ksh.1.35 million for A, B and C respectively. A 1% market share is equivalent to ksh.4 million irrespective of the firm.
Required
The firm which will have the highest annual profits in the LONG RUN (8 marks)
Explain any four assumptions you made in solving parts (a), (b) and (c) above (4 marks)
(Total: 20 marks)
QUESTION THREE
A survey concerning the qualification of employees in Kongoni ltd was carried out. Let a degree qualification be represented by A, CPA by B and CPS by C.
Nekesa, Amina, Mageto, Rop and Mwachai have degrees with Amina, Mageto, Rop and Mwachai also having CPA.
Leteipa and Mumbi have CPA with Leteipa also being a CPS holder.
Other employees with CPS qualification are Mweni, Rop and Mwachai.
Required
Represent the above data in a Venn diagram (4 marks)
What relationship is there between sets A and B? (2 marks)
What would be the suitable universal set for this probem? (2 marks)
List the members who have exactly two qualifications. (2 marks)
List the elements of the following sets and in each case, state what information is being conveyed.
AnB?C
B – A
A?B?C’
A?C
(A?C)’ (10 marks)
QUESTION FOUR
A firm produces two goods, G1 and G2, whose demand fuctions are:
P1 = 50 – q_1
P2 = 95 – 3q_2
The total cost function is
C = q_1^2 + 3q_1 q_2+ q_2^2
Required
The output level for q_1 and q_2 together with the associated prices P1and P2 which will maximize profit and the maximum profit. Ensure it is maximum. (17 marks)
Suppose there is a budget of Ksh. 800,000 for the production of G1 and G2, form the function which will give the quantities and prices to maximize profit if the budget will bee exhausted. DO NOT SOLVE. (3 marks)
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