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Management Mathematics I(Evening Class) Question Paper
Management Mathematics I(Evening Class)
Course:Bachelor Of Commerce
Institution: Kca University question papers
Exam Year:2011
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UNIVERSITY EXAMINATIONS: 2010/2011
FIRST YEAR EXAMINATION FOR THE DEGREE OF BACHELOR OF
COMMERCE
CMS 101 MANAGEMENT MATHEMATICS I
DATE: DECEMBER2011 TIME: 2 HOURS
INSTRUCTIONS: Answer Question One and Any Other Two Questions
Question One
a) A furniture workshop makes tables and chairs. The cost of making 8 tables and 5 chairs is
sh 14,000. The cost of making 3 tables and 7 chairs is sh 7,300. The workshop makes a
profit of 30% and 40% on each table and chair respectively.
i) Calculate the cost of making each table and each chair (4Marks)
ii) Calculate the selling price of each table and each chair (2Marks)
b) Write down the notation and meaning of the following set operations:
i) Union of two sets A and B (2Marks)
ii) Intersection of two sets X and Y (2Marks)
c) How many terms of a geometric progression sequence 2, 6, 18… Must be taken to give a
sum of 2186? (4Marks)
d) Compute the compound rate of interest that will yield to sh429, 981.696 after 8 years if the
initial investment was sh 100,000. (4Marks)
e) A salesman earns a fixed monthly basic salary and a commission that is directly
proportional to the number of units sold in the month. During the months of August 2011
and September 2011, the salesman’s total earnings were sh60,000 and sh70,000
respectively. The number of units sold by the salesman in the months of August 2011 and
September 2011 were 100 units and 250 units respectively. In the month of October 2011,
the salesman sold a total of 400 units.
Determine the salesman’s total earnings in the month of October 2011. (6 Marks)
f) The value of an investment has been found to behave according to the function
V = 400,000e0.1t where t is the time in years.
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i) What was the initial investment amount? (1Mark)
ii) What is the value of the investment after 5 years? (1mark)
iii) How long will it take for the value of the investment to double? (4Marks)
Question Two.
a) Explain the terms below as used in set theory
i) Power set (2Marks)
ii) Disjoint sets (2Marks)
iii) Set difference (2Marks)
b) News Agency limited deals in the distribution of three types of magazines namely; News
line, Informer and update. The company recently conducted a market survey to determine
the magazine preferences of 100 households in a certain town. The following results were
obtained from the survey:
48 households read the news line magazine.
18households read the Informer magazine.
26 households read the update magazine.
8 households read the News line and update magazines.
8 households read the News line and the Informer magazines
6 households read the update and the Informer magazines
15 households read the update magazine only
Required
i) Present the above information in a venn diagram ( 6Marks)
ii) The number that read all the three magazines (2Marks)
iii) The number of households that read the News line magazine but did not read the
informer magazine (2Marks)
iv) The number of households that read the update and the Informer magazines but did
not read the News line magazine (2Marks)
v) The number of households that read none of the three magazines (2Marks)
Question Three
a) Distinguish between an arithmetic progression sequence and a geometric progression
sequence. (4Marks)
b) Stephen started his employment with a salary of ksh240,000 per year which was increased
by sh16,000 every year upto the top of the scale of sh416,000 per year.
Required
i) In how many years time does he reach the top of the scale? (3Marks)
ii) What is the total amount he would earn during this period? (2 Marks)
c) Ayub has inherited sh 2 million from his uncle. He intends to invest the money in an
investment fund that offers an interest rate of 9% per annum.
I) Determine the accumulated amount of money after 20 years if interest is
compounded
i) Quarterly (4Marks)
ii) Semi annually (3Marks)
iii) Annually (2Marks)
II) Comment on the results obtained in I) above (2Marks)
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Question Four
a) A company produces three products; X, Y and Z which are processed through three
departments namely; P, Q and R. The table below shows the labour hours required to
produce one unit of each product in each of the departments.
Labour hours per unit
Department Product X Product Y Product Z
P 30 30 20
Q 30 20 0
R 10 30 10
The monthly labour hour capacities for the three departments are 13000, 8500 and 6000
hours for departments P, Q and R respectively. Determine the optimal combinations of the
products that could be produced with the labour hour capacities available. (8 Marks)
b) A project costs sh 16,200 and it is expected to generate the following cash inflows
Required
i) Compute the payback period of the project (2Marks)
ii) The Net present value of the project if the cost of capital is 12%. Should the project
be undertaken? (5 Marks)
iii) Estimate its internal rate of return (5 Marks)
Question Five
Baobab fabricators Ltd. have been facing a lean financial spell for the past two years. Profits
have been declining steadily and results of the preceding year showed total losses amounting to
Sh.2, 000,000, the first time the company had not reported profits in its 10 year history.
The Chairman and the board of directors have been agonizing on the remedial steps to implement
to arrest the situation. Four competing proposals have been suggested by a task force, set up some
months back, aimed at boosting sales and improving efficiency of operations in the current year.
You, as a member of the task force, have been invited to attend the next board meeting which will
deliberate on the proposals. You know the following facts:
1. The target profit for the current year is Sh.4, 000,000 regardless of the proposal that will be
adopted.
2. The company’s fixed costs currently amount to Sh.20,000,000 per year.
3. The company can sell up to a maximum of 12,000 units of its product in the local market
and unlimited quantities in a neighbouring country. For the sales in the local market, unit
variable costs amount to Sh.5, 000, while for the sales in the neighbouring country, an extra
Sh.500 per unit is incurred in transportation expenses.
4. The same selling price normally prevails both in the local market and neighbouring
country.
Year 1 2 3
Cash inflows(sh) 8,000 7,000 6,000
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5. Sales for the past year amounted to 9,000 units, all in the local market.
The main requirements of the four competing proposals are as follows:
Proposal A: The company should improve the quality of packaging of its products at a cost of
Sh.500 a unit.
Proposal B: The company should spend Sh.2,000,000 on an advertising campaign.
Proposal C: The company should cut the selling price by Sh.500 per unit
Proposal D: The company should buy efficient machinery. This would cut the variable cost per
unit by Sh.1, 000 at all levels of sales.
Required:
a) For proposals A, B and C, determine the number of units to be sold in the neighbouring
country in order t achieve the target profit. (12 Marks)
b) If proposal D is adopted and sales remain constant at 9,000 units, determine the maximum
increase in fixed machine cost if the target profit is to be achieved. (4 Marks)
c) Briefly explain four benefits of using break-even analysis. (4 Marks)
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