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Bbam 171: Management Maths Ii Question Paper
Bbam 171: Management Maths Ii
Course:Bachelor Of Entrepreneurship And Small Business Management
Institution: Chuka University question papers
Exam Year:2013
CHUKA
UNIVERSITY
UNIVERSITY EXAMINATIONS
FIRST YEAR EXAMINATION FOR THE AWARD OF
DEGREE IN BACHELOR OF ENTREPRENEURSHIP
AND SMALL BUSINESS MANAGEMENT
BBAM 171: MANAGEMENT MATHS II
STREAM: BPSM (Y1S2) BA (ENTREPRENEURSHIP) Y1 S2 TIME: 2 HOURS
DAY/DATE: WEDNESDAY 7/8/2013 8.30 A.M. – 10.30 A.M.
INSTRUCTIONS
ANSWER QUESTION ONE AND ANY OTHER TWO QUESTIONS
1. (a) Explain the meaning of the following terms.
(i) Joint probabilities
(ii) Singular Matrix
(iii) Steady state matrix [6 marks]
(b) A woman group decided to raise Kshs.480,000 to start a business venture. Before the actual payments was made. Four of the members pulled out and each of those that remained had to pay an additional Kshs. 20,000. Determine the original number of members. [5 marks]
(c) A professional football players feels that his playing career will last for the next 8 years. To prepare for his future he deposits Kshs. 35,000 at the end of each year for 8 years in an account paying 12% interest compounded semi-annually. Determine the amount he will have in his account at the end of 8 years. [6 marks]
[d] There are three urns, one black containing 3 red and 7 white marbles, one red containing 4 yellow and 6 green marbles and white containing 8 yellow and 2 green marbles. A marble is first drawn from the urn. A second marble is then drawn from the urn having the same colour as the first marble drawn. If this second marble is yellow, determine the probability that the first marble was red.
[6 marks]
(e) The following table shows the value of the random variable X and the respective probabilities P (X).
X 0 1 2 3
P (X1) ? ? ? ?
Determine the mean of X using the expectation method. [5 marks]
(f) State two assumption of Game theory. [2 marks]
2. (a) (i) Explain two reasons why a shilling today is preferred than a shilling in future. [4 marks]
(ii) Highlight two reasons for carrying out business approval. [4 marks]
(b) Beta Co. Ltd is considering the purchase of a new machine. Two alternative machines A and B have been suggested, each costing shs. 400,000. The cash flows from the machine are expected to be as follows:
Cash flows
Year Machine Machine B
1 40,000 120,000
2 120,000 160,000
3 160,000 200,000
4 240,000 120,000
5 160,000 80,000
The company has a target of return on capital of 10%.
(i) Compute the Net Present Value (NPV) and the profitability index of each machine.
(ii) State which machine you consider financially preferable. [12 marks]
3. (a) A woman save 20 dollars per month from the time she graduated at age 22 years until she retires at age 65 years. If her savings earn interest at a rate of 6.6% p.a. compounded monthly. How much does she have at retirement? [5 marks]
(b) A publishing company plans to replace a piece of equipment at an expected cost of 6500 dollars in 10 years. The company establishes a sinking fund with annual payments. The fund draws 7% interest compounded annually. Calculate the periodic payments. [4 marks]
(c) An entrepreneur wants to make an animal feeds from com, soybeans & cotton seeds. A unit of com provides 10 units of fibre, 30 units of fat and 20 units of protein. A unit of soya beans provides 20 units of fibre, 20 units of fat and 40 units of protein while a unit of cotton seed provides 30 units of fibre. 40 units of fat and 25 units of protein. Supplies needed are 1800 units of fibre, 2800 units of fat and 2200 units of protein. Model the above problem as simultaneous equation and hence use matrix method to solve the simultaneous equation so as to determine how many units at each ingredient would be needed to make the above supplies. [6 marks]
(d) A cutlery shop sells a particular cup at kshs 50 each. It purchases the cups at Kshs 30 each. At the end of the year, if the old stock is not cleared the pieces remaining are disposed at Kshs 5 each. Assuming that the demand for the cups is between 60 & 63 pieces. Draw the table for the pay off and opportunity loss for the four alternative courses of action. [5 marks]
4. (a) Given the following input. Output table
TO
FROM A B FINAL DEMAND
A 80 120 200
B 160 100 250
(i) Determine the technical coefficient matrix. [4 marks]
(ii) Determine the total output given that the consumer demand from industry A increase by 50 and that from industry B decreased by 50. [4 marks]
(b) Highlight four assumptions of Game theory. [4 marks]
(c) A theatre charges if dollars for children and 8 dollars for adults. One weekend 1000 people attended the theatre and the admission receipts totaled 6260 dollars. These can be represented by the system.
(¦(1&1@4&8)) (¦(x@y)) = (¦(1000@6260)) where
X is the number of children and y the number of adults attending. Find the number of children and adults attending. [4 marks]
(d) Discuss the significance of mathematics in business. [4 marks]
5. (a) If $100 is invested at compound interest of 8% per annum, determine
(i) The value after 10 years. [3 years]
(ii) The time correct to the nearest year it takes to reach more than $ 300. [3 marks]
(b) The value of machine originally valued at K£ 3000 depreciates at 15% p.a. calculate its value after4 years. The machine is sold when its value is less than
K£ 552. After how many years is it sold. [5 marks]
(c) Determine the future value and the amount of interest earned by a deposit of 900 shillings for 8 years at 6% compounded semi-annually. [5 marks]
(d) Highlight the meaning of the following terms.
(i) Experiment
(ii) Event
(iii) Saddle point
(iv) Zero-sum game [4 marks]
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