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Seat No.: Enrolment
GUJARAT TECHNOLOGICAL UNIVERSITY
MCA Integrated- SEMESTER- IV• EXAMINATION SUMMER 2017
Subject Code: 4440602 Date:09/05/2017
Subject Name: Operations Research
Time: 10.30 AM TO 01.00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
4. Provide Alternate Solutions wherever applicable.
Q.1

What is LPP? Discuss in brief components of an LPP. Also give its limitations.
07

Define: Operations Research. Discuss briefly features of OR. Also mention application area of OR.
07
Q.2

A manufacturer produces two different models, X and Y of the same product.
The raw materials R1 and R2 are required for production. At least 18 kg of R1
and 12 kg of R2 must be used daily. Also at most 34 hours of labour is to
be utilized. 2 kg of R1 is needed for model X and 1 kg of R1 is required for
model Y. For each model of X and 1 kg of R2 is required. It takes 3 hours to
Manufacture a model X and 2 hours to manufacture a model Y. The profit is Rs.50 for each model X and Rs. 30 for each model Y. How many units of each
model should be produced to maximize the profit? Formulate this problem as an
LP model.
07

Solve the following LPP using Simplex Method.
Max Z x1 4x2 5x3
Subject to the Constraints
3x1 3x2 22
x1 2x2 3x3 14
3x1 2x2 15
x1, x2, x3 0
07
OR

Solve the following LPP using Simplex Method.
Max Z 3x1 2x2
Subject to the Constraints
2x1 x2 2
3x1 4x2 12
x1, x2 0
07
2
Q.3 Define: Pay-off Matrix, Saddle point.
Determine the best strategies for players A and B and the value of the
game. Is this game fair? strictly determinable?
07
Determine an initial feasible solution to the following transportation problem by
using NWCM, LCM, and VAM.
Destination
Source D1 D2 D3 D4 Supply
A 11 13 17 14 250
B 16 18 14 10 300
C 21 24 13 10 400
Demand 200 225 275 250
07
OR
Q.3 Consider a problem of assigning four clerks to four tasks. The time(hours) required
to complete the task is given below:
Clerks
Tasks
A B C D
1 4 7 5 6
2 8 7 4
3 3 5 3
4 6 6 4 2
07
A machine operator has to perform three operations, turning, threading
and knurling on a number of different jobs. The time required to perform
these operations (in minutes) for each job is known and is given below:
Jobs 1 2 3 4 5 6
Time for turning 3 12 5 2 9 11
Time for threading 8 6 4 6 3 1
Time for knurling 13 14 9 12 8 13
Determine the order in which the jobs should be processed in order to
minimize the total time required to turn out all the jobs.
07
Q.4 A manufacturer has to supply his customer with 600 units of
his product per year. Shortages are not allowed and the
storage cost amounts to Rs 0.60 per unit per year. The set up
cost per run is Rs 80.00. Find the Optimum run size and the
minimum average yearly cost.
07
What is simulation? State advantages and disadvantages of simulation. 07
OR
Q.4 Define: Inventory. Explain in detail various Costs involved in Inventory. 07
3

Consider a self-service store with one cashier. Assume Poisson arrivals and exponential service times. Suppose that on average nine customers arrive every 5 minutes and that the cashier can serve 10 in 5 minutes. Find:
Average number of customers in the system.
Average number of customers queuing for service.
Average waiting time of customer in the system.
Average waiting time of customers in the queue.
Probability of no customers in the system.
07
Q.5

The initial cost of a machine is Rs. 30,000 and running or operating
expenditure which increases with age of the machine is given below:
Year
1
2
3
4
5
6
7
Running Cost(Rs.)
5000
6000
8000
10000
13000
16000
20000
What is the replacement policy? When this machine should be replaced? It is
given that the rate of interest is 10% and scrap value is nil.
07

The following maintenance job has to be performed periodically on the heat exchanges in a refinery:
Task
Immediate Predecessor
Time(Days)
A

14
B
A
22
C
B
10
D
B
16
E
B
12
F
C
10
G
C
6
H
F,G
8
I

24
J
I
16
Draw a network diagram of activities for the project.
Identify the critical path. What is its length?
Find the total float and free float for each non-critical activities
07
OR
Q.5

Give the difference between PERT and CPM.(Minimum
What do you mean by Replacement and Total Elapsed Time.
05
02

A firm is considering the replacement of a machine, whose cost price is Rs 12,200, and its scrap value is Rs 200. From experience the running (maintenance and operating) costs are found to be as follows:
Year
1
2
3
4
5
6
7
8
Running Cost(Rs.)
200
500
800
1200
1800
2500
3200
4000
When should the machine be replaced
07