# St. Joseph’s College of Commerce Operation Research Question Paper PDF Download

ST. JOSEPH’S COLLEGE OF COMMERCE (AUTONOMOUS)
END SEMESER EXAMINATION – MARCH/APRIL 2016
B.Com (T.T.) – VI SEMESTER
C2 12 602: OPERATION RESEARCH
Duration: 3 Hours                                                                                             Max. Marks: 100
SECTION – A
I) Answer ALL the questions.  Each carries 2 marks.                                        (10×2=20)
1. Give the meaning of Operation Research.
2. What do you mean by a “feasible solution” in a transportation problem?  State any 3 methods of obtaining IBFS.
3. What is an unbounded solution and a redundant solution of a LPP?
4. What is a loop in transportation problem? Draw any 2 types of loops.
5. Explain the term unbalanced and degenerancy in a Transportation Problem.
6. What is an assignment problem?
7. The Customers arrive at a booking office window every 2 minutes. It takes 1 minute for the person to serve the customer. Find Arrival rate and service rate of the queing system.
8. State the advantages of simulation.
9. Mention the steps involved in formulation of LPP.
10. List any 4 areas of LPP applications.

SECTION – B

II) Answer any FOUR questions.  Each carries 5 marks.                                      (4×5=20)
11. A firm produces two spare parts A and B using milling machine and grinding machine. The machine time required for each spare part and machine time available for each machine are given in the following table. The profit on selling each spare part is also given:

 Machines Time required per unit for Maximum time available per day Spare part A Spare part B Milling machine 10 minutes 5 minutes 2500 minutes Grinding machine 4 minutes 10 minutes 2000 minutes Profit per spare part Rs.50 Rs.100

Formulate a linear programming problem such that the number of spare parts A and B manufactured per week maximizes the profit.

12. Explain the scope of Operation Research.

13. Determine the initial basic feasible solution for the following Transportation problem by Least Cost method. The table given transportation cost from origins to destinations in ‘000s of rupees.

 Warehouses Availabilities W1 W2 W3 Factories F1 9 8 16 120 F2 15 10 17 80 F3 3 9 12 80 Requirements 150 80 50 280

14.

A company has 4 salesmen A, B, C and D. These salesmen are to be allotted to 4 districts1, 2, 3 and 4. The estimated profit per day for each salesman in each district is given in the following table. What is the optimal assignment which will yield maximum profit?

 1 2 3 4 A 16 10 14 11 B 14 11 15 15 C 15 15 13 12 D 13 12 14 15

15.

In a drive-in restaurant the arrivals follow Poisson distribution with an average of 2 cars in every 15 minutes. The restaurant  can serve the customers at the rate of 5 minutes per customer and obey exponential probability distribution. Find out  a) The probability that the service is idle.

b) Expected time that the customer has to spend in the queue.

c) Average length of the queue.

16. The daily production of mopeds in a factory varies from 146 to 154 depending upon the availability of raw material and other working conditions. The associated probabilities for various levels of production are highlighted in the following table:

 Production per day 146 147 148 149 150 151 152 153 154 Probability 0.04 0.09 0.12 0.14 0.11 0.1 0.2 0.12 0.08

The finished mopeds are transported in a specially designed lorry accommodating only 150 mopeds to the maximum. If there is any excess moped produced over and above 150, they cannot find space in the lorry and hence can be carried over to the next day’s lorry for transport. Using the following random numbers  43, 18, 26, 10, 12 simulate the production levels for 5 days and obtain the answer to the following questions:

a)      What is the average number of mopeds waiting in the factory?

b)     What will be the average number of empty spaces on the lorry?

SECTION – C

III) Answer any THREE questions.  Each carries 15 marks.                                (3×15=45)
17.  a) “Model building is the essence of OR approach”. Describe the classification  of models in detail.

b)Explain the features of Operation research

(10+5)

18. Plot a graph for the following constraints, Identify the feasible region and the Optimum solution of the LPP.

Max Z= 3x + 4y

Subject to constraints,

3x + y >= 6

x + y <=8

y<=4

x>= 2

where x, y >=0

19. Determine the initial basic feasible solution for the following transportation problem by Vogel’ Approximation Method and also find optimal solution by MODI method.

 Origins Destinations Availabilities D1 D2 D3 O1 2 8 7 100 O2 10 11 12 90 O3 5 6 9 60 O4 8 3 5 100 Requirements 80 120 150 350
20. Given the following cost matrix obtain the minimum operation time cost. Also state the optimum assignment using Hungarian method.

 Men -> Task I II III IV V A 1 3 2 3 6 B 2 4 3 1 5 C 5 6 3 4 6 D 3 1 4 2 2 E 1 5 6 5 4
21. In a market analysis, the following information was collected. Simulate for 6 trials . Workout the average profit.

RN for Selling Price         – 78, 43, 92, 87, 47, 83

RN for Unit Cost              – 23, 08, 28, 17, 73, 87

RN for sales volume        – 58, 86, 62, 06, 03, 52

 Selling Price Prob. Unit Cost Prob. Sales Volume Prob. 35 0.30 30 0.40 800 0.15 45 0.40 35 0.25 650 0.45 50 0.20 40 0.15 500 0.30 55 0.10 45 0.20 450 0.10

SECTION – D

IV) Case Study – Compulsory question.                                                                (1×15=15)
22. A departmental store has a single cashier. During the rush hours, customers arrive every 3 minutes.  The average number of customers that can be processed by the cashier is 24 per hour. Assuming that the conditions for the single channel queuing model apply, find the following

a)      Utilization rate

b)     Probability that the cashier is idle

c)      Average number of customers in the queuing system.

d)     Average time a customer spends in the system.

e)      Average number of customers in the queue.

f)       Average time a customer spends in the queue waiting for service.

g)     The number of hours the cashier is idle if he works from 9am to 6pm.

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