1
Seat No.: Enrolment
GUJARAT TECHNOLOGICAL UNIVERSITY
MCA SEMESTER-IV EXAMINATION WINTER 2018
Subject Code: 3640009 Date: 27/11/2018
Subject Name: Operations Research
Time: 10.30 am to 1.00 pm Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Q.1

Define Operations Research. List out Applications of Operations Research.
07

A company has two plants, each of which produces and supplies two products: A and B. The plants can each work up to 16 hours a day. In plant it takes three hours to prepare and pack 1000 gallons of A and one hour to prepare and pack one quintal of B. In plant it takes two hours to prepare and pack 1000 gallons of A and 1.5 hours to prepare and pack a quintal of B. In plant it costs Rs 15000 to prepare and pack 1000 gallons of A and Rs 28000 to prepare and pack a quintal of whereas in plant 2 these costs are Rs 18000 and Rs 26000, respectively. The company is obliged to produce daily at least 10 thousand gallons of A and 8 quintals of B. Formulate this problem as an LP model so as to minimize total cost of the company.
07
Q.2

Use the graphical method to solve the following LP problem.
Maximize Z 15x 10y
Subject to the constraints,
4x 6y 360 3x 180 5y 200
And y 0
07

Write down the steps of simplex method to solve the LP problem.
07
OR

Write the dual of the following primal LP problem:
Minimize Z x1 2x2
Subject to the constraints,
2x1 4x2 160 x1 x2 30 x1 10
and x1, x2 0
07
Q.3

Find the initial basic feasible solution for the following transportation problem using NWCM and LCM method:
D1
D2
D3
D4
Supply
S1
19
30
50
10
7
S2
70
30
40
60
9
S3
40
8
70
20
18
Demand
5
8
7
14
34
07

For the game with payoff matrix:
Player B
Player A
B1
B2
B3
A1

2

A2
6
4

07
2
Determine the optimal strategies for player A and B. Also determine the value of game. Is this game fair? Strictly determinable?
OR
Q.3

A department of company has five employees with five jobs to be performed. The time (in hours) that each man takes to perform each job is given in the effectiveness matrix.
Jobs
Employees
I
II
III
IV
V
A
10
5
13
15
16
B
3
9
18
13
6
C
10
7
2
2
2
D
7
11
9
7
12
E
7
9
10
4
12
07
How should the jobs be allocated, one per employee, so as to minimize the total man-hours?

Explain the structure of a Queuing System.
07
Q.4

The production department of a company requires 3,600 kg of raw material for manufacturing a particular item per year. It has been estimated that the cost of placing an order is Rs 36 and the cost of carrying inventory is 25 per cent of the investment in the inventories. The price is Rs 10 per kg. Help the purchase manager to determine an ordering policy for raw material.
07

The data collected in running a machine, the cost of which is Rs 60000, are given below:
Year
1
2
3
4
5
Resale Value
42000
30000
20400
14400
9650
Cost of spares
4000
4270
4880
5700
6800
Cost of labor
14000
16000
18000
21000
25000
07
Determine the optimum period for replacement of the machines.
OR
Q.4

Write down the steps of Simulation process.
07

Listed in the table are the activities and sequencing necessary for a maintenance job on the heat exchangers in a refinery.
Activity
A
B
C
D
E
F
G
H
I
J
Predecessor Activity

A
B
B
B
C
C
G

I
07
Q.5

Draw a network diagram of activities for the project.
Find the sequence that minimizes the total time required in performing the following jobs on three machines in the order ABC. Processing times (in hours) are given in the following table:
Job
1
2
3
4
5
Machine A
8
10
6
7
11
Machine B
5
6
2
3
4
Machine C
4
9
8
6
5
07

Explain the different inventory cost components.
07
OR
Q.5

A book binder has one printing press, one binding machine and manuscripts of 7 different books. The times required for performing printing and binding operations for different books are shown below:
Book
1
2
3
4
5
6
7
Printing time
20
90
80
20
120
15
65
Binding time
25
60
75
30
90
35
50
07
3

Decide the optimum sequence of processing of books in order to minimize the total time required to bring out all the books.
Define Events. Explain the types of Events.
03
Define Activities. Explain the types of Activities.
04