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Bcom 171: Business Mathematics Ii Question Paper
Bcom 171: Business Mathematics Ii
Course:Bachelor Of Commerce
Institution: Chuka University question papers
Exam Year:2013
CHUKA
UNIVERSITY
UNIVERSITY EXAMINATIONS
FIRST YEAR EXAMINATION FOR THE AWARD OF DEGREE OF
BACHELOR OF COMMERCE
BCOM 171: BUSINESS MATHEMATICS II
STREAMS: BCOM Y1S2 TIME: 2 HOURS
DAY/DATE: WEDNESDAY 14/8/2013 8.30 A.M. – 10.30 A.M.
INSTRUCTIONS:
Answer question 1 and any other two.
Do not write on the question paper.
Question 1 (30 Marks)
Differentiate the following terms using relevant examples
Input-Output analysis and Decision theory.
Discrete probability ad Continuous probability
Integration and differentiation [6 marks]
In a computer game, the probability that the player hits a target is 0.4. if the game goes three rounds, Find the probability that he hits the target
At least twice [2 marks]
Less than once [2 marks]
Explain the difference between mutually exclusive events and marginal probability events, as used in probability. [3 marks]
Suppose that KSh.10,000 is invested at 8% p.a compounded quarterly, how long will it take for this investment to accumulate to Ksh. 8,000? [4 marks]
Use the elimination-substitution method to solve the following system of linear equations
?4x?_1+?5x?_2-?2x?_3=21
x_1+x_2-x_3=4
? 9x?_1+?11x?_2-?5x?_3=46 [5 marks]
(i) ?¦?(?4x?^2-3x+?(1/x)) dx? [2 marks]
(ii) Given that dy/dx=?(1/2) x-5, find the value of (x,y) at which y is a maximum.
[2 marks]
State the compatibility rules using relevant examples for
Matrix addition [2 marks]
Matrix multiplication [2 marks]
Question 2 (20 Marks)
A firm was a choice between two investment projects, each of the project has an initial outlay of Sh.500,000. The return at the end of the next 4 years is given in the table below. (All values in Ksh).
Year 1 2 3 4
Project A 15000 15000 15000 14000
Project B 20000 10000 15000 5000
(i) If the interest rate is 12 ½ % p.a using NPV determine the best investment. [5 marks]
(ii) Find the IRR for project B. [4 marks]
Given that matrix B is a singular matrix find the value of x.
B = [¦(x&4@3&(x-1))] [4 marks]
(i) State and explain two advantages of studying business mathematics.
[4 marks]
(ii) Find the future value of an annuity of Sh.20,000 paid monthly at an interest
of 7% for 30 years. [3 marks]
Question 3 (20 Marks)
An electronic shop sells a particular charger at Sh.200. It purchases the chargers at Sh.120 each, but since the technology changes every year, the charger becomes obsolete and can be disposed at Sh.50. According to the past experience the annual demand for the charger is between 20 and 23 pieces. Given that the probabilities for the demand of 20 chargers is 0.07, for 21 is 0.2, for 22 is 0.4 and for 23 is 0.15, assume that the order for these chargers can be placed only once a year, the electronics manager needs to determine the number of chargers to be bought next year.
Required:
(i) Develop a pay off table. [3 marks]
(ii) Derive a regret/loss table [3 marks]
(iii) Use the expected opportunity loss to advice the manager on the number
of chargers he should buy. [4 marks]
Use Cramers rule to solve the following system of linear equations.
?3x?_1+x_2-?4x?_3=-4
-?2x?_1+?3x?_2+x_3=1
?4x?_1-?2x?_2+?3x?_3=3
[10 marks]
Question 4 (20 Marks)
A three sector economy consisting of manufacturing, Agriculture and Services had an interdependency relationship as shown in the table below.
Inputs per unit of output
From Manufacturing Agriculture Services
Manufacturing 0.3 0.2 0.4
Agriculture 0.4 0.3 0.1
services 0.1 0.2 0.1
The projected demand is 50 units, 60 units and 30 units respectively. Determine the number of units each sector should produce to satisfy the projected demand. [8 marks]
A manufacturer realizes that his revenue and total cost functions are
R=30x+20andC=x^2+16x+60
(i) State the profit function [2 marks]
(ii) Find the units (x) where he breaks even. [4 marks]
Find the units which maximize his profit. [2 marks]
What is total profit between the breakeven points? [4 marks]
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