| ST. JOSEPH’S COLLEGE OF COMMERCE (AUTONOMOUS) | ||||||||||||||||||||||||||||||||||||||||||||
| END SEMESTER EXAMINATION – APRIL 2015 | ||||||||||||||||||||||||||||||||||||||||||||
| m.com – ii semester | ||||||||||||||||||||||||||||||||||||||||||||
| P111201: OPERATIONS RESEARCH FOR BUSINESS DECISIONS | ||||||||||||||||||||||||||||||||||||||||||||
| Duration: 3 Hours Max. Marks: 100 | ||||||||||||||||||||||||||||||||||||||||||||
| SECTION – A | ||||||||||||||||||||||||||||||||||||||||||||
| I) | Answer any SEVEN questions. Each carries 5 marks. (7×5=35) | |||||||||||||||||||||||||||||||||||||||||||
| 1. | The Costs and Selling Prices per unit of two products manufactured by a Company are as under:
In any month, the maximum availability of inputs is limited to the following: Direct Materials – 480 kgs, Direct Labour Hours – 400 hours and Painting Hours – 200 hours. Formulate a Linear Programming Problem to determine the Production Plan which Maximizes the profit. (Do not solve) |
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| 2. | Explain the Dynamic Programming Approach of solving an OR problem. Briefly explain any three applications of DPP. | |||||||||||||||||||||||||||||||||||||||||||
| 3. | Write the Dual of the following LPP
Min Z= 3x + 4y + 8Z Subject to, 2x + y +10z ≥ 50 x + y = 5 x ≤ 3 Where x, y, z ≥ 0 |
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| 4. | Discuss the significance of introducing slack, surplus and artificial variables in Simplex Method? What meaningful information can be derived from them? | |||||||||||||||||||||||||||||||||||||||||||
| 5. | A hospital pays nurses for 40 hours a week. One nurse is assigned to one patient. The cost per hour for each of the nurses is given below:
(i) Find the nurse-patient combination to minimize cost to the hospital. (ii) How much does each nurse earn per week?
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6. |
Find the initial solution using NWCM and LCM for the following transportation problem.
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7. |
A belt snapping for conveyors in an open cast mine occur at the rate of 2 per shift. There is only one hot plate available for vulcanising, and it can vulcanise on an average 5 belts snap per shift. (a) What is the probability that when a belt snaps, the hot plate is readily available. (b) What is the probability of having exactly 3 belts waiting for service in the system? (c) What is the average waiting time plus vulcanising time? |
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8. |
A Car Rental Agency has collected the following data on the demand for five-seater vehicles over the past 50 days.
The Agency has only 6 cars currently.
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9. |
Explain any five OR techniques mentioning their areas of application. |
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10. |
How do you deal with the following conditions while solving a Transportation Problem – Degeneracy, Unbalance, Prohibited Route. |
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SECTION – B |
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| II) | Answer any THREE questions. Each carries 15 marks. (3×15=45) | |||||||||||||||||||||||||||||||||||||||||||
| 11. | Solve the following LPP by Big M Method.
Max Z = 10x + 12y Subject to, x + y = 5 x ≥ 2 y ≤ 4 where x, y ≥ 0 |
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12. |
Plot the graph of the LPP given below and identify the optimum solution Max Z = 0.1 x + 0.2 y Subject to constraints, x + y ≤ 10 x ≤ 7 y ≤ 7 -2x + 3y ≤ 0 Where x, y ≥ 0
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| 13. | The transportation cost matrix for a given situation for supply of the commodity from sources A, B, C to the points of usage P, Q and R is given below. Work out the optimal cost solution for the problem using Vogel’s Approximation method and Modified distribution method. Does the problem have multiple solution . If yes find the solution.
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14. |
A marketing manager has five salesmen and five sales districts. Considering the capabilities of the salesmen and nature of districts, the marketing manager estimates that sales per month (in thousand rupees) for each salesman in each district would be as follows –
Find the assignment of salesmen to districts that will result in maximum sales. |
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15. |
A departmental store has a single cashier. During the rush hours, customers arrive at the rate of 20 customers per hour. The average number of customers that can be processed by the cashier is 24 per hour. Assume that the conditions for the use of single channel queuing model apply. What is the (a) Probability that the cashier is idle? (b) Average number of customers in the queuing system? (c) Average time a customer spends in the system? (d) Average number of customers in the queue? (e) Average time a customer spends in the queue waiting for service? |
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SECTION – C |
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| III) | Case Study (1×20=20) | |||||||||||||||||||||||||||||||||||||||||||
| 16. | ABC Company is considering the question of marketing a new product. The fixed cost required in the project is Rs. 4,000. Three factors are uncertain viz., the Selling Price, Variable Cost and Annual Sales Volume. The product has a
life of only one year. The management has the data on these three factors as under.
Simulate the average profit for the above project on the basis of 5 trials.
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