Janardan Rai Nagar Rajasthan Vidyapeeth 2007 B.Tech Aeronautical Engineering BTAE5-OPERATION RESEARCH - Question Paper

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BACHELOR OF TECHNOLOGY
(SEMESTER – V)(AERONAUTICAL/BIO-TECHNOLOGY/CHEMICAL/CIVIL/MARINE/MECHANICAL/MINING/METALLURGY)

BTAE5/BTBT5/BSCH5/BTC5/BTMR5/BTM5/BTMI5/BTMT5-OPERATION RESEARCH

TIME: 03 HOURS
MAX. MARKS: 75
GENERAL INSTRUCTIONS:
1. Question paper is divided into 3 groups
2. Each group is of 25 marks every
3. Figure to the right in bracket shows mark
4. Assume suitable data if necessary

GROUP A: ans any 3 ques.. ques. No. one is compulsory.
Q.1 Define operation research and discuss scope of OR in management. (05)
Q.2 (i) What is a Queuing problem? explain a few of the basic components in a waiting line. (ii) discuss the characteristics of a Queuing system. (10)
Q.3 What is the difference ranging from PERT and CPM? describe the terms: Slack, Total float, free float and independent float. (10)
Q.4 What is linear programming? elaborate its major limitations? define 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 2 kinds 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 1 insertion is desired in 1 problem. At lowest five 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: ans any 3 ques.. ques. No. six is compulsory.
Q.6 Find the optimal solution for the assignment issue with subsequent 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 issue
Maximize Z= 3x1 +10x2 + 2x3
Subject to 2x1 +3x2 +2x3 <=7
3x1 – 2x2 +4x3 =3
x1>=0, x2>=0,x3>=0
(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 subsequent precedence relationships:
A, C, D can begin immediately;
E>B, C ;
F, G >D ;
H, I >E, F ;
J> I, G ;
K >H; B >A (10)
Q.9 Explain subsequent for a transportation issue
(a) lowest cost method (b) Vogel’s approximation method
(c) Degeneracy (d) MODI method (10)
Q.10 find the critical path and project duration for the subsequent PERT
network. (10)











GROUP C: All ques. are Compulsory.
Q.11 Fill in the blanks (each ques. carries two 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 __________ issue
(iv) CPM stands for __________.
(v) __________ is an event oriented technique.

Q.12 Multiple option ques.. (Each ques. carries two marks)
(i) Queuing theory is associated with
(a) Inventory (b) Sales
(c) sales (d) production
(ii) The expected time is provided 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 provided 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 issue

Q.13 True or false (each ques. carries one mark).
(i) Network analysis is synthesis of 2 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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Earning:   Approval pending.