Download JNTUH (Jawaharlal nehru technological university) MCA (Master of Computer Applications) 2nd Sem (Second Semester) Regulation-R15 2017 August 821AJ Operations Research Previous Question Paper
R15
Code No: 821AJ
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
MCA II Semester Examinations, August - 2017
OPERATIONS RESEARCH
Time: 3hrs
Max.Marks:75
Note: This question paper contains two parts A and B.
Part A is compulsory which carries 25 marks. Answer all questions in Part A.
Part B consists of 5 Units. Answer any one full question from each unit. Each
question carries 10 marks and may have a, b, c as sub questions.
PART - A
5 ? 5 Marks = 25
1.a) What are the artificial variables? Explain their importance.
[5]
b) State the degeneracy in transportation problem. How is it resolved?
[5]
c) State and explain the optimal replacement policy when time and money value is
considered.
[5]
d) Explain the terms i) Saddle point ii) MaxMin and Min max criterion iii) Strategies. [5]
e) Explain about various associated costs of inventory.
[5]
PART - B
5 ? 10 Marks = 50
2.a) Define model. Classify the models with respect to their physical configuration.
b) The manufacturer of patent medicines is proposed to prepare a production plan for
medicines A and B. There are sufficient ingredients available to make 20,000 bottles of
medicine A and 40000 bottles of medicine B but there are only 45000 bottles into which
either of medicines can be filled. Further, it makes three hours to prepare enough material
to fill 100 bottles of medicine A and one hour to prepare enough material to fill 1000
bottles of medicine B and there are 66 hours available for this operation. The profit is
Rs.8 per bottle for medicine A and Rs.7 per bottle for medicine B. Formulate this problem
as a LPP in order to maximize profit and solve it by graphical method.
[4+6]
OR
3.
Solve the LPP problem by Big M method:
Max Z 4x 5x 3x 50
1
2
3
st x x x 10
1
2
3
x x 1
1
2
2x 3x x 40 x 0 i
1
2
3
i
[10]
4.a) Give the mathematical formulation of a transportation problem.
b) Use North-west corner method to obtain an initial basic feasible solution of the
transportation problem & find the optimal solution.
[4+6]
W
X
Y
Z
Supply
Warehouse
Factory
A
11
13
17
14
250
B
16
18
14
10
300
C
21
24
13
10
400
Demand
200
225
275
250
OR
5.a) State the optimality and reduction theorems for solving the assignment problems.
b) A company has a team of four salesmen and there are four districts where the company
wants to start its business. After taking into account the capabilities of salesmen and the
nature of districts, the company estimates that the profit per day in rupees for each
salesman in each district is as below.
Districts
D1 D2 D3 D4
S1 16 10 14 11
Sales man S2 14 11 15 15
S3 15 15 13 12
S4 13 12 14 15
Find the assignment of salesmen to various districts which will yield profit?
[4+6]
6.
The time spent in hours in processing two jobs on six machines A, B, C, D, E and F and
the necessary technological orderings of machines are as follows.
Job 1:
A.20 C.10 D.10 B.30 E.25 F.15
Job 2:
A:10 C.30 B.15 D.10 F.15 E.20
Use graphic method to determine an optimal sequence of jobs which minimizes the
elapsed time.
[10]
OR
7.
The following failure rates have been observed for a certain type of light bulbs:
End of week Probability of failure to date
1
0.05
2
0.13
3
0.25
4
0.43
5
0.68
6
0.88
7
0.96
8
1.00
The cost of replacing an individual failed bulb is Rs.1.25. The decision is made to replace
all bulbs simultaneously at fixed intervals and also to replace individual bulbs as they fall
in service. If the cost of group replacement is 30 paise per bulb, what is the best interval
between group replacement? At what group replacement price per bulb would a policy of
strictly individual replacement become preferable to the adopted policy?
[10]
8.
Solve the following LPP by dynamic programming approach
Max Z x 9x
1
2
[10]
st
2x x 25
1
2
x ,
11
x 0 i
2
i
OR
9.a) State and explain the dominance principles.
b) Solve the following game using dominance property.
[4+6]
Player B B1 B2 B3
Player A
A1
1 7 2
A2
6 2 7
A3
5 2 6
10.a) Derive an expression for EOQ when demand rate is uniform, production rate is finite and
shortages are not allowed
b) If a product is to be manufactured within the company, the details are as follows:
Annual demand rate, =24000 units
Production rate, K=48000 units
Setup cost, Cr=Rs. 200 per setup
Carrying cost, Cc= Rs.20/unit/year.
Find the i) EOQ and ii) Cycle time.
[4+6]
OR
11.a) Explain about various types of customers in the queuing system
b) In a bank, cheques are cashed at a single "teller" counter. Customers arrive at the counter
in a Poisson manner at an average rate of 30 customers/hr. The teller takes on an average
1.5 minutes to cash a cheque. The service time has been shown to be exponentially
distributed.
i) Calculate the percentage of time the teller is busy
ii) Calculate the average time a customer is expected to wait.
[4+6]
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This post was last modified on 17 March 2023