Download JNTUH (Jawaharlal nehru technological university) MCA (Master of Computer Applications) 2nd Sem (Second Semester) Regulation-R132019 December 812AK Operations Research Previous Question Paper
R13
Code No: 812AK
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
MCA II Semester Examinations, December - 2019
OPERATIONS RESEARCH
Time: 3 Hours
Max. Marks: 60
Note: This question paper contains two parts A and B.
S Part A is compulsory which carries 20 marks. Answer all questions in Part A. Part B
consists of 5 Units. Answer any one full question from each unit. Each question carries 8
marks and may have a, b, c as sub questions.
PART - A
5 ? 4 Marks = 20
1.a)
What are the main characteristics of OR? Explain with suitable examples.
[4]
b)
Show that assignment model is a special case of transportation model.
[4]
c)
What are the various simplifying assumptions made while dealing with sequencing
problems?
[4]
d)
Explain Saddle point, Value of the game, Two-person zero-sum game and strategy.
[4]
e)
Given average arrival rate = 8 /hour, average service time = 5 minutes,
calculate
i) utilization factor ii) Idle time
iii) Probability that a customer arriving at the service counter will have to wait
iv) Probability that the number of customers in the system is 2.
[4]
PART - B
5 ? 8 Marks = 40
2.a)
Solve the L.P.P. by the simplex method:
Maximize Z = 40x1 + 35 x2
Subject to 2x1 + 3x2 60,
4x1 +5 x2 96
x1 , x2 0.
b)
Use graphical method to solve
Maximize Z = 6x1 + 8 x2
Subject to 5x1 + 10x2 60
4x1 + 4x2 40
x1 , x2 0.
[4+4]
OR
3.
Use the two-phase method to solve the problem:
Minimize Z = x1- 2x2 - 3x3 ,
Subject to -2x1 + x2 +3 x3 = 2,
2x1 +3 x2 +4 x3 = 1,
x1 , x2 , x3 0.
[8]
4.a)
Write the procedure for U ? V method.
b)
A factory has three warehouses W1, W2 and W3 which supply to four stores S1, S2, S3
and S4. Monthly capacities of the warehouses are W1 = 100 units, W2 = 40 units and
W3 = 60 units. Monthly demands at the stores are S1 = 30 units, S2 = 50 units, 3=65units
and S4= 55 units. The shipping cost in terms of rupees from warehouses to stores is as
given below:
S
Stores
Warehouses
S1
S2
S3
S4
W1
14
16
12
20
W2
12
14
10
8
W3
10
16
8
15
The problem here is to determine the optimum distribution for the factory to minimize
shipping costs.
[4+4]
OR
5.a)
A department store has leased a new store and wishes to decide how to place four
departments in four locations so as to maximize total profits. The table below gives the
profits, in thousands of Rupees, when the departments are allocated to the various
locations. Find the assignment that maximizes total profits.
Location
1
2
3
4
Shoes
20
16
22
18
Departments Toys
25
22
18
28
Auto
27
20
26
23
House wares 24
22
23
22
b)
A travelling salesman, named Rolling Stone plans to visit five cities 1, 2, 3, 4 & 5. The
travel time (in hours) between these cities is shown below:
To
From
1
2
3
4
5
1
5
8
4
5
2
5
7
4
5
3
8
7
8
6
4
4
4
8
8
5
5
5
6
8
How should Mr. Rolling Stone schedule his touring plan in order to minimize the total
travel time, if he visits each city once a week?
[4+4]
6.a)
Shahi Export House has to process five items through two stages of production, viz,
cutting & sewing. Processing times are given in the following table:
Items
Time In Hours
Cutting
Sewing
A
7
4
S
B
3
8
C
11
9
D
5
10
E
12
6
Determine an order in which these items should be processed so as to minimize the total
processing time.
b)
Two jobs are to be performed on five machines A, B, C, D, and E. Processing
times are given in the following table. Use graphical method to obtain the total minimum
elapsed time.
[4+4]
Machine
Job 1
Sequence
:
A
B
C
D
E
Time
:
4
5
3
7
3
Sequence
:
B
C
A
D
E
Job 2
Time
:
6
5
4
3
7
OR
7.
The failure rates of transistors in a computer are summarized in Table
Failure rates of Transistors in computers
End of the week
1
2
3
4
5
6
7
Probability of failure to date 0.07 0.18 0.30 0.48 0.68 0.89 1
The cost of replacing an individual failed transistor is Rs. 9. If all the transistors are
replaced simultaneously, it would cost Rs. 3.00 per transistor. Any one of the following
two options can be followed to replace the transistors:
a) Replace the transistors individually when they fail (individual replacement policy).
b) Replace all the transistors simultaneously at fixed intervals and replace the individual
transistors as they fail in service during the fixed interval (group replacement policy).
Find out the optimal replacement policy, i.e. individual replacement policy or
group replacement policy. If group replacement policy is optimal, then find at what equal
intervals all the transistors should be replaced.
[8]
8. Resolve the reliability problem for the following data. Total capital available c = 15.
S
[8]
OR
9.a)
Two firms are sompeting for business under the conditions such that one firm's gain is
another firm's loss. Firm A's payoff matrix is given below. Suggest optimal strategies
for the two firms and the net outcome thereof.
b)
Solve the following game by reducing them to 2 ? 2 games by graphical method [4+4]
B
A
3
4
0
1
2
-1
5
-2
2
3
10.a) A textile mill boys its raw material from a vendor. The annual demand of the raw
material is 9000 units. The ordering cost is Rs. 100 per order and the carrying cost is
20% of the purchase price per unit per month, where the rchase price per unit is Rs. 1.
Find i) Economic order quantity
ii) Total cost w.r.t. EOQ
iii) Number of orders per year iv) Time between consecutive two orders.
b) A company manufactures refrigeration units in batches. The estimated demand is
12,000 units/year. It costs Rs. 100 to setup the manufacturing process and the carrying
cost is Rs. 0.75 per unit per year. Once the production process has been setup, 90 units
can be manufactured daily. The demand during the production day has been 65 units per
day. How many units should the company produce in each batch? How long will the
production cycle last?
[4+4]
OR
11. The arrival rate of customers at a banking counter follows Poisson distribution with a
mean of 45 per hour. The service rate of the counter clerk also follows Poisson
distribution with a mean of 60 per hour.
i) What is the probability of having 0 customers in the system?
ii) What is the probability of having 5 customers in the system?
iii) What is the probability of having 10 customers in the system?
iv) Find Lq, Ls, Wq and Ws
[8]
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This post was last modified on 17 March 2023