DISTANCE EDUCATION
M.C.A./MCA (Lateral) DEGREE EXAMINATION,
DECEMBER 2017.
Fourth Semester
RESOURCE MANAGEMENT TECHNIQUES
(2005 to 2010 calendar year)
Time Three hours Maximum 100 marks
Answer any FIVE questions.
All questions carry equal marks.
x 20 100)
1. Write down the procedure for mathematical
formulation of linear programming problem.
Old hens can be bought for Rs. each but the
young ones cost Rs. each. The old hens lay 3
eggs per week, each being worth Rs. A hen costs
Rs. 100 per week to feed. If I have only Rs. to
spend for hens, how many of each kind should I buy
to give a profit of more than Rs. per week,
assuming that I cannot house more than 20 hens?
Write a mathematical model of the above problem.

sp4
3. Four professors are each capable of teaching any one of
four different courses. Class preparation time in hours for
different topics varies from professor to professor and is
given in the table below
Professor Linear
programmes
Queueing
theory
Dynamic
programme
Regression
analysis
A 2 10 9 7
B 15 4 4 8
C 13 14 16 11
D 4 15 13 9
Each professor is assigned only one course so as to
minimize the total course preparation time for all course.
Use Hungarian method to solve the problem.
4. Discuss on Queueing system with infinite
population model.
The railway marshalling yard is sufficient only for
9trains (there being 10 lines, one of which is
earmarked for the shunting engine to reverse itself
from the rest of the hump to the rear of the train).
Trains arrive at the rate of 30 trains per day,
inter-arrival time follows an exponential
distribution and service time distribution is also
exponential with an average of 36 minutes.
Calculate the following.
The probability that the yard is empty
The average time length.
5. Dr STRONG is a dentist who schedules all her patients
for 30 minutes appointments. Some of the patients take
more or less than 30 minutes depending on the type of
dental work to be done. The following summary shows
the various categories of work, their probabilities and the
time actually to complete the work.
Category Time required (minutes) Probability of category
Filling 45 0.40
Crown 60 0.15
Cleaning 15 0.15
Extraction 45 0.10
Check up 15 0.20
DE-2757
3
sp4
Simulate the dentist's clinic for four hours and
determine the average waiting time for the patients
as well as the idleness of the doctor. Assume that
are the patients show up at the clinic at exactly
their scheduled arrival time starting at 8.00 AM.
Use the following random numbers handling the
above problem
40 82 11 34 25 66 17 79
6. Write about inventory costs and analysis.
The annual demand of a particular item by a
company is 10,000 units. This item may be obtained
from either an outside supplier or subsidiary
company. The relevant data for the procurement of
an item are given below
Costs From outside
supplier
From subsidiary
company
Cost per unit 12 13
Cost of placing an order 10 10
Cost of receiving an order 20 15
Storage and all carrying
costs, including capital cost
per unit per annum
2 2
What purchase quantity and from which source
would you recommend to procure?
What would be the minimum total costs in that
case?
DE-2757
4
sp4
7. A small project is composed of seven activities whose time
estimates are listed in the table as follow
Activity Estimated duration (weeks)
i j Optimistic Most
likely
Pessimistic
1 2 1 1 7
1 3 1 4 7
1 4 2 2 8
2 5 1 1 1
3 5 2 5 14
4 6 2 5 8
5 6 3 6 15
Draw the project network.
Find the expected duration and variance of each
activity.
Calculate early and late occurrence times for each
event. What is the expected project length?
Calculate the variance and standard deviation of
project, Length. What is the probability that the
project will be completed
At least 4 weeks earlier than expected.
No more than 4 weeks later than expected.
8. A manufacturer is offered two machines A and B. A is
priced at Rs. 5,000 and running costs are estimated at
Rs. 800 for each of the first five years, increasing by
Rs. 200 per year in the sixth and subsequent years.
Machine B which has the same capacity as costs Rs.
2,500 but will have running costs of Rs. 1,200 per year for
six years, increasing by Rs. 200 per year thereafter.
If money is worth 10% per year, which machine should
be purchased? Assume that the machines will eventually
be sold for scrap at a negligible price.