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Buss 320: Quantitative Techniques In Business Question Paper
Buss 320: Quantitative Techniques In Business
Course:Quantitative Techniques In Business
Institution: Kenya Methodist University question papers
Exam Year:2008
KENYA METHODIST UNIVERSITY
END OF FIRST TRIMESTER 2008 EXAMINATION
FACULTY : BUSINESS AND MANAGEMENT STUDIES
DEPARTMENT : BUSINESS ADMINISTRATION
COURSE CODE : BUSS 320
COURSE TITLE : QUANTITATIVE TECHNIQUES IN BUSINESS
TIME : 3 HOURS
INSTRUCTIONS:
• Answer any FOUR questions
Question 1
a) Define the following terms as used in input-output analysis.
i) Inter industry transactions
ii) Primary inputs
iii) Technical coefficients (6marks)
b) Given the following input – output table below:
TO
From A B Consumer demand
A 140 200 400
B 300 200 600
Primary inputs 300 700
i) Find the technical coefficient matrix.
ii) Determine the total output given that the consumer demand from industry A increased by 100 and that the industry B decreased by 50. (10marks)
c) Solve the following set of simultaneous equations using Cramer’s rule;
2x – y = 10
-3x + z = 15
-4x + 3z = 12 (9marks)
Question 2
a) Distinguish between assignment and transportation problems. (4marks)
b) A certain industry has four subsidiary companies whose accounts are to be audited. The company has short-listed five audit firms that can be assigned any of the audit tasks.
The table below shows the fees charged by the audit firms to audit the accounts of the respective subsidiary companies.
Subsidiary Companies
Audit Mayfair Hitech Alpha Omega
Firm (sh.million) (sh.million) (sh.million) (sh.million)
A 5 10 16 10
B 18 14 12 16
C 10 13 14 12
D 13 6 10 16
E 14 11 8 13
i) The assignment the company would make to minimize the total cost of auditing the subsidiary companies. (12marks)
ii) The audit firm which will not be assigned any task. (1marks)
iii) The minimum cost of auditing the subsidiary companies. (3marks)
c) State and explain any five queue disciplines. (5marks)
Question 3
a) Explain the following terms as used in network analysis;
i) dummy variable
ii) Backward pass
iii) Earliest start times
iv) Critical path activities
v) Floats (10marks)
b) Consider the following project network and activity time (in weeks)
B E D
C J
F H I
A
G
Activity Activity times (weeks)
A 5
B 3
C 6
D 6
E 7
F 3
G 10
H 8
Required:
i) How long will it take to finish this project? (7marks)
ii) Can activity (i) be delayed without delaying the entire project? If so, by how many weeks? (1mark)
iii) What is the schedule for activity E? (2marks)
c) State any five rules of drawing networks. (5marks)
Question 4
a) Some consultants have estimated the demand curve of a client’s firm to be;
AR = 200 – 8Q
Where AR is average revenue in millions of shillings and Q is the output in units. Investigations have further shown that the firms cost profile have a marginal cost (MC) given by MC = Q2 – 28Q + 211 (in million of shillings).
Further investigations have shown that the firm’s cost when not producing output is sh.10 million.
Required:
i) The equation of total cost. (5marks)
ii) The equation of total revenue. (2marks)
iii) An expression for profit. (2marks)
iv) The level of output that maximizes profit. (5marks)
v) The equation of marginal revenue. (2marks)
b) Evaluate the following:
i) Derivative of 4x3 – 2. (2marks)
ii) Derivative of 4x(2x-1)2 (2marks)
iii) (2marks)
iv) (3marks)
Question 5
a) State and briefly explain any five assumptions of game theory. (10marks)
b) Outline five requirements of linear programming. (5marks)
c) A firm produces two products A and B. The manufacturing activities require 3 inputs; raw materials, man hours and machine hours. Each unit of product A requires 8 units of raw materials, 12 units of man hours and 6 units of machine hours. Each unit of product B requires 16 units of raw materials, 4 units of man hours nad 12 units of machine hours. The firm has available the following levels of inputs namely raw materials 32 units, manhours 54 units and machine hours 20 units. If product A and product B contribute 10/= and 16/= respectively towards profits.
i) If the objective of the firm is to maximize profits formulate the above problem as a linear programming problem.
ii) Calculate the maximum profits. (10marks)
Question 6
a) Briefly outline the steps involved in the process of simulation. (9marks)
b) Given the following matrices:
A = B =
C =
Determine:
i) A -1
ii) BC
iii) AB
iv) BA
v) 2A – B (10marks)
c) Given the following sets of expressions in a two commodity market, determine the equilibrium values of prices and quantities.
Qd1 = 24 – 18P1 + 18P2
Qd2 = 36 – 12P1 + 12P2
Qs1 = -18 + 6P1
Qs2 = -12 + 12P2 (6marks)
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