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Posted Date: 26 Nov 2008 Posted By:: maxx Member Level: Bronze Points: 5 (₹ 1)
2007 Janardan Rai Nagar Rajasthan Vidyapeeth B.Tech. Mining Engineering BTAE5-OPERATION RESEARCH University Question paper
BOT - V TOTAL PAGES: 03
BACHELOR OF TECHNOLOGY
(SEMESTER – V)(AERONAUTICAL/BIO-TECHNOLOGY/CHEMICAL/CIVIL/MARINE/MECHANICAL/MINING/METALLURGY)
TIME: 03 HOURS
MAX. MARKS: 75
1. Question paper is divided into three groups
2. Each group is of 25 marks each
3. Figure to the right in bracket indicates mark
4. Assume suitable data if necessary
GROUP A: Answer any three questions. Question No. 1 is compulsory.
Q.1 Define operation research and explain scope of OR in management. (05)
Q.2 (i) What is a Queuing problem? Discuss some of the basic components in a waiting line. (ii) Explain the characteristics of a Queuing system. (10)
Q.3 What is the difference between PERT and CPM? Define the terms: Slack, Total float, free float and independent float. (10)
Q.4 What is linear programming? What are its major limitations? Describe its applications in any functional areas of management. (10)
Q.5 A marketing manager wishes to allocate his annual advertising budget of
Rs.20,000 in two types of media A and B. The unit cost of a message-in media A is Rs.1,000 and that of B is Rs. 1,500. Media A is a monthly magazine and not more than one insertion is desired in one issue. At least 5 messages should appear in media B. The expected effective audience for unit message in the media A is 40,000 and for media B is 55,000.
(a) Develop a mathematical model.
(b) Solve it for maximizing the total effective audience. (10)
GROUP B: Answer any three questions. Question No. 6 is compulsory.
Q.6 Find the optimal solution for the assignment problem with following cost matrix: (05)
W X Y Z
A 11 17 8 16
B 9 7 12 6
C 13 16 15 12
D 14 10 12 11
Q.7 (a) Construct the dual of the problem
Maximize Z= 3x1 +10x2 + 2x3
Subject to 2x1 +3x2 +2x3 <=7
3x1 – 2x2 +4x3 =3
(b) Maximize Z= 5x1 + 8x2
subject to 3x1 + 5x2 <=18
5x1 + 3x2 <= 14
x1,x2 >=0 (10)
Q.8 Draw a network diagram for the following precedence relationships:
A, C, D can start immediately;
E>B, C ;
F, G >D ;
H, I >E, F ;
J> I, G ;
K >H; B >A (10)
Q.9 Explain following for a transportation problem
(a) Least cost method (b) Vogel's approximation method
(c) Degeneracy (d) MODI method (10)
Q.10 Obtain the critical path and project duration for the following PERT
GROUP C: All Questions are Compulsory.
Q.11 Fill in the blanks (each question carries 2 marks)
(i) Operation Research introduce __________ into decision analysis
(ii) In queuing theory __________ distribution is denoted by M.
(iii) North West Corner Method is used for __________ problem
(iv) CPM stands for __________.
(v) __________ is an event oriented technique.
Q.12 Multiple choice question. (Each question carries 2 marks)
(i) Queuing theory is associated with
(a) Inventory (b) Sales
(c) sales (d) production
(ii) The expected time is given by
(a) te = (t0 + 4tm + tp) / 6 (b) te = (4t0 + tm + tp) / 6
(c) te = (t0 + tm + 4tp) / 6 (d) te = (to + tm + tp)
(iii) Optimization can be applied to
(a) Linear programming (b) Transportation
(c) Assignment (d) Routing
(iv) Recorder Level is given by
(a) Lead time demand + safety stock (b) EOQ + Lead Time demand
(c) Safety stock + EOQ (d) None of the above
(v) Hungarian method is used for
(a) LPP (b) Material handling
(c) Assignment Problem (d) Queuing problem
Q.13 True or false (each question carries 1 mark).
(i) Network analysis is synthesis of two techniques namely CPM and PERT
(ii) In a PERT chart only critical activities are numbered.
(iii) Vogel's approximation method is the best method to get initial b.f.s.
(iv) A transportation model must form a square matrix.
(v) Queuing theory is associated with waiting time.
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