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Management Mathematics I Question Paper
Management Mathematics I
Course:Bachelor Of Commerce
Institution: Kca University question papers
Exam Year:2011
1
UNIVERSITY EXAMINATIONS: 2010/2011
FIRST YEAR EXAMINATION FOR THE DEGREE OF BACHELOR OF
COMMERCE
CMS 101: MANAGEMENT MATHEMATICS I
DATE: AUGUST 2011 TIME: 2 HOURS
INSTRUCTIONS: Answer question ONE and any other TWO questions
Question One
a) Briefly but clearly explain how linear functions can be used to determine the market equilibrium
Point (3 Marks)
b)Explain the importance of set theory in a business environment (3 Marks)
c)A manufacturer makes two products i.e product Q and product M. The cost of making 15 units of
product Q and 10units of product M is sh 600. The cost of making 5 units of product Q and 8
units of product M is sh 340. Determine the cost of making each product. (6 Marks)
d)Mia Shillings Department Stores is planning to open a store in Westlands. It has asked the
Superior Marketing Company (SMC) to do a market study of randomly selected families within
a five kilometer radius of the store. Among the questions it wishes SMC to ask each home
owner are: (i) family income, (ii) family size, (iii) distance from home to the store site.
Required:
2
For each of the three questions, develop a random variable of interest to Mia Shillings
Department Stores.Denote which of these are discrete and which are continuous random
variables. (4 Marks)
e) If sh 80,000 is deposited to earn 10% interest for 3 years and then 12% per annum in the
subsequent years, what would be the total amount of deposit on the basis of compound interest at
the end of 5 years? (4 Marks)
f) The value of an investment has been increasing at an exponential rate of 10% per annum.
Specifically, the value of the investment is described by the function,
v = 600, 000e0.1t where t is the time in years.
i) What is the principal investment (2 Marks)
ii) What is the expected value of the investment after 8 years (3 Marks)
iii)How long will it take for the value of the investment to double (5 Marks)
Question Two
a) A patient recovering from a certain illness requires to have daily at least 18 units of Vitamin A and
at least 9 units of vitamin E. The vitamins are available in both the tablet and the capsule form.
Each tablet contains 4 units of Vitamin A and 1 unit of Vitamin E. Each capsule contains 2 units
of vitamin A and 3 units of vitamin E. By letting x and y be the number of tablets and the number
of capsules respectively required daily.
Required
i) Write down all the inequalities satisfied by x and y. (3 Marks)
ii) Illustrate the solution set of the inequalities on the graph (2 Marks)
iii)If the total number of tablets and capsules combined is to be minimum, how many of
each should be taken daily? (3 Marks)
iv)If each tablet cost sh1 and each capsule cost sh2.50, calculate the minimum cost per
day (2 Marks)
b) Nyakio , Kerubo and Auma are business women who deal with the purchase and sale of green
groceries. Recently, the three business women travelled to molo town to purchase the green
groceries for sale. Nyakio purchased 2 bags of potatoes, 6 boxes of tomatoes and 5 bags of
mangoes at a total cost of sh20,200. Kerubo purchased 10 bags of potatoes, 4 boxes of tomatoes
and 1 bag of mangoes at a total cost of sh21,800. Auma purchased 1 bag of potatoes, 7 boxes of
3
tomatoes and 6 bags of mangoes at a total cost of sh 21,900.The cost incurred in transporting the
groceries from molo town was sh.100 per bag of potatoes, sh150 per box of tomatoes and sh.120
per bag of mangoes. The business women sold the green groceries at sh.1,800 per bag of potatoes,
sh.1,600 per box of tomatoes and sh.2,500 per bag of mangoes.
Required
i) The prices at which the businesswomen purchased 1 bag of potatoes, 1 box of
tomatoes and 1 bag of mangoes in molo town. (4 Marks)
ii) The transportation cost incurred by each of the three business women (3 Marks)
iii)The profit earned by the three business women. (3 Marks)
Question Three
a) The following information relates to a dealer in standard wooden tables. The dealer realized a
profit of sh 12,000 from sale of 7 tables, sh12,400 from sale of 9 tables and sh11,300 from the sale
of 4 tables. The profit function is believed to be quadratic in \nature.
Required
i) Derive the profit function (7 Marks)
ii) How much profit would be realized if 12 tables are sold. (3 Marks)
b) A survey was conducted on the newspaper readership of 3 dailies; National Daily, Standard News
and Timely Newspapers, N, S and T respectively and the following data was obtained:
?? The number of people who read N, S and T were found to be 55, 45 and 39 respectively.
?? The number that read N and K = 19
?? The number that read S and N = 15
?? The number that read S and K = 14
?? Those who read all the 3 were found to be 4 people only
Required:
Determine the number of people who:
i) Read the National Daily only (4 Marks)
ii) Read Standard News or Timely but not National Daily (3 Marks)
iii)The total number of people interviewed if 5 people read none of the papers.(3 Marks)
Question Four
4
a) Mrs Mali mingi has designed a saving scheme as follows; She saves sh1 on the first day, sh2 on
the second day, sh4 on the third day and so on, doubling the amount every day. Find the total
amount saved at the end of the month of January under this scheme. (6 Marks)
b) The cost of a motor vehicle is sh 200,000. If depreciation is charged at 20% of the value at the
beginning of every year, find out after how many years the value will be sh65, 536. (8 Marks)
c) The population of a country increases at an average compound rate of 3.5% p.a. If the population
at the beginning of year 2010 was 20 million, what will be the population at the end of year 2014?
(6 Marks)
Question Five
a) State and explain three classification of investment projects (3 marks)
b) A project has an initial cost sh 6 million . It is expected to have an economic life of 5 years after
which it will have a residual value of zero. Earnings before depreciation and tax from the project
are expected as follows:
Year 1 2 3 4 5
Earnings before depreciation and
Tax(sh”millions”)
2.8 3.0 3.2 3.8 4.0
The corporate tax rate is 30% and depreciation is on a straight line bases. The firm’s cost
of capital is 15%.
Required
i) Annual cash flows after tax. (8 Marks)
ii) Net present value of the project. (8 Marks)
iii)Should the project b e undertaken? (1 Mark)
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