Business Mathematics 2 (MGTC3204)
Higher Institute of Commerce and Management (HICM)
Semester: Second Semester
Level: 300
Year: 2015
UNIVERSITY OF BAMENDA
Second semester examination
Higher institute of commerce and Management
Academic year 2014/2015
Date:_______________
Time allowed : 3 hours
Venue,
Examiner: Prof Njimanted, G.F
Course code: MGTC204
Course Title: Business Maths II
Credit Value: 6
Instructions: Answer question 2(two) and any other questions in this paper. Orderly presentation of results will
yield student full marks.
1) Find the limits of the following functions
A) f(x) =
as x2 (2 mks)
b) f(x) =
as x6 …………………………………………………………………………………. (2
mks)
c) f(x) =
as x6 (3 mks)
d) f(x) =
as x∞ (3 mks)
e) State the conditions for the continuity of a function and verify whether the function f(x) =
is continous at
the point x=3
2a) if y=4
. Find
and evaluate your result when x=1 (10 mks)
2b) find the relative maximum, minimum and point of inflexion for the function (10 mks) y=20 + 24x + 2
2c) Given the average production function of a manufacturing firm in Douala as AP
L
=
+ 5L +
i) Deriver the firm’s total production function and marginal product (2 mks)
ii) Plot the graph of the AP
1
, TP
1
and the MP
1
for 0 L10 and comment on the nature of your result. (8
mks)
3a) Given the boundary condition y=11 when x=3. Find the function whose first derivative result is (5
mks)
b) Evaluate the function
(5 mks)
c) If the marginal revenue of a firm is given as
-10x +100, find the total revenue and the average revenue of
the firm within the range of output of 0 and 10. (5mks)
d) Calculate the marginal product of labour (MP
1
) is represented by the function MP
i
=8L + 30.Find the total and
average production functions of labour. (5mks)
Q4a) Find the cofactor, adjoint and inverse of the following matrices
A=
!
" , and C=
# $
%
" d= &
'
( )
*
+ (10 mks)
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Q4b)Given the equations, (i) represents a market demand function and (ii) a market supply function. The
variables of the system are quantity (q) and market price p; q=15-2p…………..(i); q= 10 + 3p………(ii). Solve
the equations to determine equilibrium price and quantity using the matrix algebra method (10 mks)
5a) A monopoly firm has to sell its product in two markets-market 1 and market 2. The price function for the
two markets is given as follows;
P
1
= 500-q
1
P
2
= 300-q
2
The monopoly firm’s total cost(TC) function is given as TC=50, 000 + 100q. You are required to find. (i) The
profit maximizing output (ii) the allocation of the OP between the two markets (iii) The equilibrium price for
each market. (iv) The profit of the maximizing output. (10 marks)
(5b) If firms under monopolistic competition face a uniform demand function as given below; TC= 100-0.5P
1
and their total cost (TC) function is given as TC= 1562.50 + 5q-,
+ 0.05,
when new firms enter the industry,
the demand function is given as P=98.75-P
2.
(a) what account for the new firm to enter the industry? (b) how are
the equilibrium price and output of the old firms affected by the entry of the new firms.
(10mks)
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