Download BU (Bangalore University) MBA 2nd Semester 2016 July Quantitative Techniques Operational Research Question Paper

PG-923

II Semester M.B.A. Degree Examination, July 2016

(CBCS)

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MANAGEMENT

2.6: Quantitative Techniques and Operation Research

Time: 3 Hours

Max. Marks: 70

SECTION-A

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Answer any five of the following. Each question carries five marks. (5x5=25)

1. Distinguish between Analytical and Simulation Models.
2. A firm is considering replacement of a machine whose cost price is Rs. 12,200 and the scrap value is Rs. 200. The maintenance costs are found from experience to be as follows:
   

   Year	1	2	3	4	5	6	7	8
   Maintenance Cost (Rs.)	200	500	800	1200	1800	2500	3200	4000

   What is the optimal replacement interval for this machine?
3. Five jobs are to be processed and five machines are available. Any machine can process any job with resulting. Profit (in Rs.) as follows. Find assignment pattern that maximizes the sales.
   

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   	A	B	C	D	E
   1	70	75	71	60	80
   2	55	57	64	61	50
   3	60	54	80	71	55
   4	80	72	75	65	70
   5	50	56	70	51	72

   Jobs
   Machines
4. Explain the essential features of queuing system.
5. What is degeneracy? How it can be resolved in case of Transportation?
6. Find out the sequence that minimizes the total elapsed time required in performing the following tasks on machine M1 and M2 in the order M1, M2. Also, find the minimum total elapsed time.
   

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   Task	A	B	C	D	E	F	G	H
   M1	5	4	9	6	8	7	5	4
   M2	6	8	7	4	3	9	8	11

7. Moon Light Bakery keeps stock of a popular brand of cake. Previous experience indicates the daily demand as given here.
   

   Daily Demand	0	10	20	30	40	50
   Probability	.01	.20	.15	.50	.12	.02

   Consider the following sequence of random numbers.
   R. No. 48, 78, 19, 51, 56, 77, 15, 14, 68, 09.
   Simulate the demand for next 10 days. Find out the stock situation if the owner of the bakery decides to make 30 cakes every day. Also estimate the daily average demand for the cakes on the basis of simulated data.

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SECTION-B

Answer any three of the following questions each question carries ten marks. (10x3=30)

8. National Oil Co. has three refineries and 4 depots. Transaction costs per barrel and requirements are given below. Determine optimal allocation of output.
   

   	D1	D2	D3	D4	Capacity
   R1	5	7	13	10	700
   R2	8	6	14	13	400
   R3	12	10	9	11	800
   Requirement	300	600	700	400

9. "Operation Research is the application of Scientific Methods, techniques and tools to problems involving in the operations of a system so as to provide those in control of the systems with optimum solution to the problems." Discuss with suitable examples.

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10. Determine the dominance principle of game theory using the following:
    

    	B1	B2	B3	B4
    A1	15	35	25	5
    A2	10	20	5	0
    A3	20	50	10	5
    A4	25	55	15	20

    Firm B
    Firm A
11. A project consists of eight activities with the following relevant information:
    

    Activities	Immediate Predecessor	Optimistic	Most Likely	Pessimistic
    A	---	1	1	7
    B	---	1	4	7
    C	A	2	2	8
    D	B	1	1	1
    E	B	2	5	14
    F	C	2	5	8
    G	D,E	3	6	15
    H	F,G	1	2	3

    Estimated Duration (Days)
    1. Draw the PERT network and determine critical path.

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    2. If a 30 days deadline is imposed, what is the probability that the project will be finished within the time?
    3. If the project manager wants to be 99% sure that the project is completed on the scheduled date, how many Weeks before that date should he start the project work?

SECTION-C

12. Case Study (Compulsory): (1x15=15)

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A company manufactures three types of parts which use precious metals platinum and gold. Due to shortage of these precious metals, the govt. regulates the amount that may be used per day. The relevant data with respect to supply requirements and profit are summarized in the table shown below:

Daily allotment of platinum and gold are 160 gm and 120 gm respectively. Determine the optimum profit under Simplex Method.

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