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Management Mathematics Ii Question Paper

Management Mathematics Ii

Course:Diploma In Business Management

Institution: Kca University question papers

Exam Year:2012

UNIVERSITY EXAMINATIONS: 2009/2010
STAGE III EXAMINATION FOR DIPLOMA IN BUSINESS MANAGEMENT
DMS 102: MANAGEMENT MATHEMATICS II
DATE: DECEMBER 2009 TIME: 1½ HOURS
INSTRUCTIONS: Answer any THREE questions
QUESTION ONE
(a) Two TV stations Citizen and Kiss compete for viewers. Of those who view Citizen on a given
day, 35% view Kiss the next day. In the case of those who view Kiss on a given day, 25% switch
over to Citizen the next day. Suppose yesterday, of the total viewers 55% viewed Citizen and the
rest Kiss, determine the percentage of viewers for each station:
(i) Today [2 Marks]
(ii) Tomorrow [2 Marks]
(iii) In the long run (equilibrium/steady state) [4 Marks]
(b) A group of physical fitness devotees works out in the gym every day. The workouts vary from
strenuous to moderate to light. When their exercise routine was recorded, the following
observation was made: Of the people who work out strenuously on a particular day, 40% will
work out strenuously on the next day and 60% will work out moderately. Of the people who work
out moderately on a particular day, 50% will work out strenuously and 50% will work out lightly
on the next day. Of the people working out lightly on a particular day, 30% will work strenuously
on the next day, 20% moderately, and 50% lightly.
(i) Set up the 3 × 3 transition matrix with columns and rows labeled S, M, and L that
describes these transitions. [2 Marks]
(ii) Suppose that on a particular Monday 80% have a strenuous, 10% a moderate, and 10% a
light workout. What percent will have a strenuous workout on Wednesday? [4 Marks]
2
(iii) What will the proportion of physical fitness devotees who will be working out in each of
the three categories in the long run? [6 Marks]
QUESTION TWO
(a) Briefly explain the applications of techniques of calculus in business. [6 Marks]
(b) The following expressions define a firm’s total revenue and total cost functions:
Total revenue (Sh.’000’) (R) = 18x – x2 + 24
Total cost (Sh.’000’) (C) = ? x3 – 2.5x2 + 50
Where x is the number of units produced and sold
(i) Use calculus method to find the profit maximization production level. [6 Marks]
(ii) State the firm’s profits at the optimum production level. [2 Marks]
(c) Max Ltd. employed a cost accountant who developed two functions to describe the operations of
the firm. He found the marginal revenue function to be MR = 25 – 5x – 2x2 and the marginal cost
function to be MC = 15 – 2x – x2 where x is the level of output. Find the level of profit
maximization. [6 Marks]
QUESTION THREE
( ) the following Matrices
7 5 8 4
and
9 4 7 5
a Given
A B
? - ? ? ?
= ? ? = ? ? ? ? ? - ?
Find
(i) BA [3 Marks]
(ii) (AB)-1 [4 Marks]
(iii) Determinant of (8B - 3A) [3 Marks]
(b) Solve the following System of equations simultaneously using the inverse matrix method
3x – 4y + 2z = - 4
4x + 2y – 5z = 9
2x+ 3y + 3z = 16 [10 Marks]
QUESTION FOUR
(a) Find the first derivative of the following
(i) y = 7x3 + 5x2 – 3x + 6 [1 Mark]
3
(ii) y = (6x2 + 2x)(4x - 8) using product rule [4 Marks]
(iii) y = (2x + 5)/ (3x2 – 7x + 3) using quotient rule [4 Marks]
(b) Evaluate the following integrals
(i) ?(7x3 + 2x2 - 5x)dx [2 Marks]
(ii) ( ) 3
2
1
? 7x - 3x + 7 dx [3 Marks]
(c) A firm sells two products which cost £10 and £15 to produce. The profit function is
considered to be, p =60x + 150y – x² - 3y².
Determine the values of x and y which will maximize profit. [6 Marks]
QUESTION FIVE
(a) Distinguish between input-output analysis and Markov analysis. [6 Marks]
(b) List the assumptions behind Input-Output analysis. [4 Marks]
(c) A conglomerate has three divisions, which produce computers, semiconductors, and business
forms. For each Sh.1 of output, the computer division needs Sh.0.02 worth of computers,
Sh.0.20 worth of semiconductors, and Sh.0.10 worth of business forms. For each Sh.1 of
output, the semiconductor division needs Sh.0.02 worth of computers, Sh.0.01 worth of
semiconductors, and Sh.0.02 worth of business forms. For each Sh.1 of output, the business
forms division requires Sh.0.10 worth of computers and Sh.0.01 worth of business forms. The
conglomerate estimates the sales demand to be Sh.30, 000,000 for the computer division,
Sh.10, 000,000 for the semiconductor division, and Sh.20, 000,000 for the business forms
division.
Required:
(i) The technical coefficient matrix [2 Marks]
(ii) Leontiff matrix [2 Marks]
(iii) Given that the Leontiff inverse matrix is:
1.036 0.023 0.105
0.209 1.015 0.021
0.109 0.023 1.021
? ?
? ?
? ?
? ?
? ?
Find the level each division should produce in order to satisfy this demand? [6 Marks]

Management Mathematics Ii Question Paper

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