Download AKTU B-Tech 7th Sem 2018-2019 NOE 073 Operations Research Question Paper

Download AKTU (Dr. A.P.J. Abdul Kalam Technical University (AKTU), formerly Uttar Pradesh Technical University (UPTU) B-Tech 7th Semester (Seventh Semester) 2018-2019 NOE 073 Operations Research Question Paper

Printed Pages: 04 Subject Code: NOE073
Paper Id: 199703 Roll No:
BTECH
(SEM VII) THEORY EXAMINATION 2018-19
OPERATIONS RESEARCH
Time: 3 Hou rs _ Total Marks:100
Notes: Assume any Missing Data.
SECTION - A
1. Attempt all questions in brief. 2 x 10 = 20
What is the role of operations research in decision making?
"Dual ofa dual is it?s primal" Explain.
Degeneracy in a transportation problem.
What are assignment problems? Give two examples.
What is float? What are the different types of ?oat?
What is looping and dangling in network diagram?
What is two person zero-sum games?
Characteristics of M/M/] queue model.
Discuss the various costs involved in an inventory model
Write a lucid note on replacement problem.
Hermenogocrw
- SECTION - B
2. Attempt any three of the following: 10 x 3 = 30
a. Three machine shops A, B, C produces three types of products X, Y, Z respectively. Each
product involves operation of each of the machine shops. The time required for each
operation on various products is given as follows:
Machine Shops
Products A B C Pro?t per unit
X 10 7 2 Sl2
Y 2 3 4 33
Z l 2 1 51
Available Hours 100 77 80
The available hours at the machine shops A, B, C ate 100, 77, and 80 only. The pro?t per
unit of products X, Y, and Z is $12, $3, and $l respectively.
b Find the optimal solution of the following transportation problem in which cell entries
represent unit costs.
Market
~ I II 111 Supply
Ware A 4 l4 8 10
House B 6 6 2 16
C 10 8 [4 14
D 2 2 4 28
Requirement 14 18 36 68

c. The following table shows the various jobs of a network along with their time estimates:
Activim Estimated Duration work
Optimistic Most Likely Pessimistic
1 -2 1 1 7
1 -3 I 4 7
2-4 2 2 8
2?5 1 l 1
3-5 2 5 l 4
4-6 2 5 8
5-6 3 6 l 5
6-7 2 4 8
Draw a network diagram and determine the critical path. What is the minimum time for
completion of projects?
(1. What do you understand by queuing model? Why do arrivals and services follow the
Poisson and Exponential distribution respectively?
e. The demand for an inventory item each costing ReS, is 20000 units per year. The ordering
cost is Rs. 10. The inventory carrying cost is 30% based on the average inventory per year.
Stock out cost is R55 per unit of shonage incurred. Find out various parameters.
SECTION - C
Attempt any one part of the following: '
a Solve the following LPP
Maximize Z= 5X1 + 10 X2 +8 X3
Subject to the following constraints ::
3 Xi+5 X2 +2 X3 360 -
4 Xi+4 X2 +4 X3 S 72 -*'
2Xi+4 X2 +5 X3 5 100 ?
b What is sensitivity analysisiDiscuss its signi?cance from managerial viewpoint.
Write the dual of the fougmng primal problem:
Maximize Z = - 52:42x2
Subjectto : Xi?; 72 2
2XH-3X2 S 5
Xi, X2 2 0
10x1=10
Attempt any one part of the following: 10 x 1 = 10
a. A wholesale company has three warehouses from which retail customers. The company
deals in a single product, the supply of which at each warehouse are
Conveniently, total su?ply?at the warehouses is equal to customers. The following table gives
Warehouse Nu. Supplv unln Customer No. Demand units
1 20 A 15
ll 28 B 19
II I 17 C 13
D 18
the transportation cost per unit shipment from each warehouse to each customer :