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Management Mathematics Ii Question Paper
Management Mathematics Ii
Course:Diploma In Business Management
Institution: Kca University question papers
Exam Year:2010
UNIVERSITY EXAMINATIONS: 2009/2010
STAGE III EXAMINATION FOR DIPLOMA IN BUSINESS MANAGEMENT
DMS 102: MANAGEMENT MATHEMATICS II
DATE: APRIL 2010 TIME: 1½ HOURS
INSTRUCTIONS: Answer any THREE questions
Question One
a) Find the order and transpose of the following matrices
i. (8, -8, 5, 3) ii. 1 3 5
6 4 2
0 1 2
4 6 3
5 1 2 (4 Marks)
b) Given the matrices A = 10 15 and B = 21 13 find
20 14 12 17
i) A + B
ii)A - B (4 Marks)
c) Briefly define the following terms:
i) Symmetric matrix
ii) Diagonal matrix
iii) Unit matrix
iv)Null matrix (4 Marks)
d) Given the matrix A = 1 2 3 Find A-1
3 -4 -2
5 3 5
2
Hence solve the following system of equations using inverse method
x1 + 2x 2 + x3 = 4
3x1 – 4x2 – 2x3 = 2
5x1 + 3x2 + 5x3 = -1 (8 Marks)
Question Two
a) Identify three application areas of matrices (3 Marks)
b) Using an appropriate rule, find the derivatives of the following functions (6 Marks)
i) Y = (2x2 + 10x + 5 ) (6x3 + 12x2)
ii) Y = 10x2 + 6x + 5
12x3 + 15x2
iii) y = (10x2 + 6x)3 (6 Marks)
c) Find the partial derivative of Z = 10 + 3x – 4x2 + 10y – 2y2 + xy (5 Marks)
Question Three
a) If y = 2x2 – 8x + 50 , find dy , hence establish whether the turning point to the curve is
dx
maximum or minimum (6Marks)
b) Consider a monopolist with two products, A and B. Maximize the total profit given that the two
demand functions are PA = 80 – qA, PB = 50 – 2 qB and the total cost function is
TC = 100 + 8qA + 6qB + 14 qB
2 + 4qA
2 + 4q a qB
Also find the level of profit and the prices charged for the two products A and B (10 Marks)
c) Differentiate each of the following functions
i. x = 7y + 2y2 – 4y3
ii. r = 2S + 4S2 + S1/2 (4 Marks)
Question Four
a) If average revenue (AR) for a company is given by
AR = 100 – 2X , (x is quantity),
3
Find the marginal revenue (MR) function and the price when MR = 0 (8 Marks)
b) Suppose the total costs (TC) for the company in (a) is given by the following function
TC = 1/3 x3 – 5x2 + 30 x , (x is quantity) Find the average cost (AC) and marginal cost (MC)
Functions (8 Marks)
c) Using the information in parts (a) and (b) above, find the quantity levels where
i. AR = AC; and
ii. MR = MC (4 Marks)
Question Five
a) A company’s profit function is given by
Profit, II = -2X2 + 40X + 10, (x = output).
Determine the profit maximizing output level for the company, checking that the second order
conditions are met. (6 Marks)
b) If a firms total costs (TC) are related to its workforce and capital equipment by the function
TC = 1OL2 + 1OK2 – 25L – 50K – 5LK + 2000
Where L is thousands of employees and K is thousands of pounds invested in capital, find the
combination of labour and capital to give minimum total cost? Find this cost and show that it
is minimum (6 Marks)
c) Solve the following systems of equations using Cramer’s rule
i. 3x – 2y – z = 2
-4x + y – z = 3
2x +0y + z = 1 (8 Marks)
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