Operations Research B.Tech Question Paper : vardhaman.org

College : Vardhaman College Of Engineering
Degree : B.Tech
Department : Aeronautical Engineering
Semester : VI
Subject : Operations Research
Document type : Question Paper
Website : vardhaman.org

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Operations Research Question Paper :

Four Year B. Tech VI Semester Regular Examinations June – 2014
(Regulations: VCE-R11)
(Aeronautical Engineering)
Date: 8 June, 2014
Time: 3 hours
Max Marks: 75
Answer ONE question from each Unit

Related : Vardhaman College Of Engineering Finite Element Methods B.Tech Question Paper : www.pdfquestion.in/6385.html

All parts of the question must be answered in one place only :

Unit – I :
1. a) List and Explain phases of Operations Research. 7M
b) Solve the following LPP by Simplex method.
Minimize Z= 5×1 +6 x2
S.T. 2×1 +5×2 ? 1500
3×1 +x2 ? 1200
x1 ,x2 ? 0
8M

2. a) Explain unbounded solution and infeasible solution. 6M
b) The furniture shop manufacturing desks and chairs. The following table gives the resources required and their availability. The profit per desk is Rs 30 and per chair is Rs 0. Determine number of tables and chairs to be manufactured to maximize profit.
Resource Availability Requirements
Per desk Per chair
Carpentry (man-hours) 200 8 4
Upholstery (man hours) 120 – 3
Wood (m3 ) 17 0.5 0.4
Laminate (m3 ) 20 1 –

Unit – II :
3. a) Explain degeneracy in transportation problem and how to resolve it? 5M
b) A company has 3 plants located at different places but producing an identical product and supply to 3 warehouses. The warehouse capacity is 80, 110 and 150. The plant capacity is 150, 10 and 130. The table below gives profit matrix between factories and warehouses. Find the distribution pattern to maximize profit/minimize loss. Profit matrix: 10M
W1 W2 W3
F1 6 6 3
F2 -2 -2 -4
F3 3 2 2

4. a) Differentiate between transportation problem and assignment problem. 5M
b) Given the matrix of setup cost, show how to sequence production so as to minimize setup cost per cycle. 5M
A1 A2 A3 A4 A5
A1 8 2 5 7 1
A2 6 8 3 8 2
A3 8 7 8 4 7
A4 12 4 6 8 5
A5 1 3 2 8 8

Unit – III :
5. a) There are 5 jobs each of which has to go through the machines A and B in the order A, B.
The processing times are given below. Determine the sequence of these jobs that will minimize total elapsed time. 5M
Job 1 2 3 4 5
Machine A 5 1 9 3 10
Machine B 2 6 7 8 4

b) Find the optimum sequence that minimizes the total time required for completing the following jobs on machines processed in order CBA. Determine the corresponding elapsed time and idle time for each machine.10M
Job 1 2 3 4 5 6
Machine A 8 7 6 9 10 9
Machine B 3 4 5 2 1 6
Machine C 8 3 7 2 5 1

6. a) Explain Kendall notation for single server queuing system with infinite capacity. 5M
b) The time spent on processing 2 jobs on 5 machines and the necessary technological sequence of operations are as follows:
Job 1: A-2 to B-3 to C-4 to D-3 to E-2.
Job 2: C-4 to A-2 to B-6 to E-2 to D-5
Determine the minimum elapsed time for completing both the jobs and the sequence of jobs on each machine.

Unit – IV :
7. Electronic equipment consists of 500 resistors, when any resistor fails, it is replaced. The cost of replacing a resistor individually is Rs 20. If all resistors are replaced at the same time, the cost per resistor is Rs 5. The percentage surviving, S(i) at end of month “I” is given in table. 15M
Month, i 0 1 2 3 4 5
S(i) 100 90 75 55 30 0
What is the optimum replacement plan? 15M

8. a) An aircraft manufacturing company uses certain parts at a constant rate of 2500/year. Each unit costs Rs 30, the company estimates that it costs Rs 130 to place an order and inventory carrying cost is 10% per year. How frequently should order be placed? Also determine optimum size of the order. 8M
b) Illustrate deterministic demand model with uniform and production rate infinite of inventory management and derive the EOQ formula. 7M

Unit – V :
9. a) Explain forward and backward recursive function. 3M
b) A corporation is entertaining proposals from its 3 plants for possible expansion facilities. The corporation is budgeting Rs 5 million for allocation for all 3 plants. The following table summarizes the costs and revenues. Zero cost proposals are introduced to allow for probability of not allocating funds to individual plants. Maximize the revenues resulting from allocation to plants. Use forward recursive method.
PROPOSAL Plant-I Plant-II Plant-III
Cost-1 Revenue-1 Cost-2 Revenue-2 Cost-3 Revenue-3
1 0 0 0 0 0 0
2 1 5 2 8 1 3
3 2 6 3 9 – –
4 – 0 4 12 – –

10. a) Explain the following with respect to game theory: strategy, mixed strategy, pure strategy, saddle point. 8M
b) A B
1 2 3
I -4 6 3
II -3 -3 4
III 2 -3 4
Solve the above game.