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Sit 404 Question Paper
Sit 404
Course:Bachelor Of Science In Information And Technology
Institution: Kenyatta University question papers
Exam Year:2011
KENYATTA UNIVERSITY
UNIVERSITY EXAMINATIONS 2010/2011
EXAMINATION FOR THE DEGREE OF BACHELOR OF SCIENCE
(INFORMATION TECHNOLOGY)
SIT 404: MANAGEMENT MATHEMATICS
DATE: THURSDAY, 7TH JULY 2011
TIME: 11.00 A.M. – 1.00 P.M.
INSTRUCTIONS: Answer Question ONE and any other TWO Questions.
Question 1
(30 marks)
a)
Determine the equation of the line perpendicular to but with the same x – intercept as
the line
(3 marks)
b)
Compute the following limit
i)
ii)
(
)
(6 marks)
c)
Calculate the derivatives from first principles, for the following functions
i)
ii) v
(6 marks)
d)
Using the completion of square method, solve
(3 marks)
e)
Determine the stationary points of
i)
ii)
(6 marks)
Page 1 of 4
f)
Solve the following system of simultaneous equations.
(3 marks)
g)
A firm’s demand function is given by
and it’s cost function
Determine the optimal level of output for profit maximization.
(3 marks)
Question 2
(20 Marks)
a)
Given the function
, determine the critical
values and test the nature of optimality of function at these points.
(6 marks)
b)
A computer manufacturer estimates that the annual rate of expenditure for
maintenance on one of its brands is represented by the function
i) Of the above expenditures, what is expected to be incurred during the fifth year?
ii) What are the expected maintenance expenditures during the computer’s first 5 years?
(8 marks)
c)
A hospital blood bank conducts an annual blood drive to replenish its inventory of
blood. The hospital estimates that blood will be donated at a rate of pints per
day, where
and equals the length of the blood drive in days.
If the goal for the blood drive is 2,000 pints, when will the hospital reach its goal?
(6 marks)
Page 2 of 4
Question 3
(20 Marks)
a)
Given
, and
, find,
i)
and at
ii)
The Marginal revenue and Marginal cost.
iii)
The Marginal profit.
(6 marks)
b)
It is known that the number of units demanded is given by
Find,
i)
The Total revenue function, TR
ii)
The Marginal revenue, MR at
(5 marks)
c)
Show that for compound interest the relationship between the amount accruing
(future value) , principal , and time and rate is given by
(4 marks)
d)
Draw the graph of the inequality below simultaneously and show the wanted region.
[
(5 marks)
Question 4
(20 Marks)
a)
The marginal revenue function for a company’s product is
.
Where is the number of units equals produced and sold. If total revenue
equals 0 when no units are sold, determine the total revenue function.
(4 marks)
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b)
The resale value of a piece of industrial equipment has been found to behave
according the function
where is years since original purchase.
i) What is the original value of the piece of equipment?
ii) What is the expected resale value after 5 years?
(8 marks)
c)
A factory produces calculators per day the total daily cost incurred is
. If the calculators are sold for Ksh.
each, find the
number of calculators that would maximize the daily profit.
(8 marks)
Question 5
(20 Marks)
a)
Given
v ; find,
i)
ii)
ii)
(6 marks)
b)
Given
, determine the critical values and test the nature of
optimality of the function at these points.
(6 marks)
c)
Evaluate the following integrals;
i)
?
ii)
?
(4 marks)
d)
Assume that a company has a marginal profit function given by
,
where is in £s and is the sales in units. If the company breaks even on sales
of 5 units. What are the fixed costs of the company?
(4 marks)
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