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Seat No.: Enrolment
GUJARAT TECHNOLOGICAL UNIVERSITY
MCA SEMESTER-IV- EXAMINATION WINTER 2018
Subject Code: 640003 Date: 22/11/2018
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 the following terms:
Operations Research
Objective Function
Events
EOQ
Idle Time on a Machine
Failure
Optimal solution
14
Q.2

Use graphical method to solve the following LP problem.
Maximize
Subject to constraints
360
180
200
And 0
07

Solve the following LP problem using Simplex Method.
Max z
Subject to the constraints
430
460
420
And 0
07
OR

A company makes two products P and using two machines A and B). Each unit of P that is produced requires 50 minutes processing time on machine A and 30 minutes processing time on machine B. Each unit of Q that is produced requires 24 minutes processing time on machine A and 33 minutes processing time on machine B. Machine A is going to be available for 40 hours and machine B is available for 35 hours. The profit per unit of P is $25 and the profit per unit of Q is $30. Formulate this problem as an LP model to determine the production quantity of each product in such a way as to maximize the total profit, given that the available resources should not be exceeded.
07
Q.3

Construct the dual of the problem
Minz
Subject to



10,
07
2
2


And

0.

Explain the various steps involved in solving transportation problem using
North West Corner Method Least Cost Method.
07
OR
Q.3

Find the initial basic feasible solution of the following transportation problem:
NWCM LCM
Plants
Ware houses
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
07

A book binder has one printing press, one binding machine and manuscripts of a number of books. The time required for performing the printing and binding operations on each book are shown below. The binder wishes to determine the order in which the book should be processed, so that the total time required to process all books is minimized.
Book
1
2
3
4
5
6
Printing time (Hours)
30
120
50
20
90
110
Binding time (Hours)
80
100
90
60
30
10
07
Q.4

What is Simulation? Explain the advantages and disadvantages of Simulation.
07

Define the terms: Saddle Point Value of the Game Fair Game
ii) Find the range of values of p and q which will render the entry(2,2) a saddle point for the game
Player B
2
4
5
10
7
q
4
p
6
03
04
OR
Q.4

Explain the structure of the Queuing System.
07

An Accounts Officer has 4 subordinates and 4 tasks. The subordinates differ in efficiency. The tasks also differ in their intrinsic difficulty. His estimates of the time each would take to perform each task are given in the matrix below. How should the tasks be allocated one to one man, so that the total man hours are minimized?
Task
subordinate
I
II
III
IV
1
8
26
17
11
2
13
28
4
26
3
38
19
18
15
4
19
26
24
10
07
Q.5

What is Replacement? Explain the types of failures with example.
07

A small assembly plant assembles PCs through 9 interlink stages according to the following precedence process.
Stages
From
1
1
1
2
2
3
4
5
6
6
7
8
To
2
3
4
4
5
6
6
7
7
8
8
9
07
3
Hours
4
12
10
8
6
8
10
10
0
8
10
6
Draw an Arrow Diagram (Network) representing the above assembly work.
Tabulate Earliest Start, Earliest Finish, Latest Start and Latest Finish time for all the stages.
Find the Critical Path and the Assembly Duration.
Tabulate the Total Float, Free Float and Independent Float.
OR
Q.5

Explain the difference between PERT and CPM.
07

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% of the inventories. The price is Rs. 10 per kg. Help the purchase manager to determine an ordering policy for raw material.
07