ST. JOSEPH’S COLLEGE OF COMMERCE (AUTONOMOUS) |
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| END SEMESTER EXAMINATION – MARCH/APRIL 2016 | ||||||||||||||||||||||||||||||||||||||||||||||||||||
| m.com ii semester | ||||||||||||||||||||||||||||||||||||||||||||||||||||
| P115 AR 201:QUANTITATIVE TECHNIQUES AND OPERATIONS RESEARCH | ||||||||||||||||||||||||||||||||||||||||||||||||||||
| Duration: 3 Hours Max. Marks: 100 | ||||||||||||||||||||||||||||||||||||||||||||||||||||
| SECTION – A | ||||||||||||||||||||||||||||||||||||||||||||||||||||
| I) | Answer any SEVEN questions. Each carries 5 marks. (7×5=35) | |||||||||||||||||||||||||||||||||||||||||||||||||||
| 1. | A manufacturing unit has three products on their production line. The production capacity for each product is 50, 30 and 45 respectively. The limitation in the production shop is that of 300 manhours as total availability and the manufacturing time required per product is 0.5,1.5 and 2.0 manhours. The products are priced to result in profits of Rs.10, 15 and 20 respectively. If the company has a daily demand of 25 units, 20 units and 35 units for respective products, formulate the problem as LP model so as to maximize the total profit.
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| 2. | Find initial solution to the following transportation problem using Least Cost Method.
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| 3. | What is a Travelling Salesman Problem? How is it solved?
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| 4. | State the addition and multiplication theorem on probability.
Probability that a contractor will get a building contract is ¼. And the probability of not getting a road contract is 2/3. If the probability of getting both the contracts is is 2/5, find out the probability that he will get either of the two contracts.
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| 5. | Based on the weather conditions and industrial development in a new industrial belt, the demand for petrol for vehicles on a new service station follows the under mentioned distribution.
Beginning of every week storage of petrol is 3500 liter. Simulate for 5 weeks to show the inventory at the end of the week and unsatisfied demand Random Nos: – 23, 78, 95, 05, 29
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| 6. | Customers arrive at the first class ticket counter of a theatre at a rate of 12 per hour. There is a clerk who can service the customer at the rate of 30 customers per hour. Find
a) Average length of the queue. b) Average waiting time in the system. c) The free time of the clerk if he works for 8 hours a day.
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| 7. | Payoff of three acts X,Y,Z and states of nature L, M, N are given below:
The probabilities of the states of nature are 0.3, 0.4, and 0.3 respectively. Calculate the expected monetary value (EMV) for different acts & select the best act.
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| 8. | A company dealing with newly invented telephonic device is faced with the problem of selecting the following strategies:
i) Manufacture the device itself, ii) To be paid on a royalty basis by another manufacturer, iii) Sell the rights for its invention for a lump sum. The profit is thousands of rupees that can be expected in each case and the probabilities associated with the sales volume are shown in the following table:
Represent the company’s problem in the form of a decision tree and identify the best decision.
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| 9. | Find initial solution to the Transportation problem by VAM and check for degeneracy.
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| 10. | State Baye’s Theorem. In a bolt factory macines A, B and C manufacture 25, 35 and 40 percent of the bolts. Out of the total of their output 5, 4 and 2 percent are defective. A bolt is drawn at random and is found to be defective. What is the probability that it was manufactured by machine B. | |||||||||||||||||||||||||||||||||||||||||||||||||||
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SECTION – B |
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| II) | Answer any THREE questions. Each carries 15 marks. (3×15=45) | |||||||||||||||||||||||||||||||||||||||||||||||||||
| 11. | Solve graphically
Maximize Z= 80x + 120 y Subject to constraints, 20x +50 y ≥300 x + y ≤ 9 x ≥ 2 y ≥ 1 where x , y≥0
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| 12. | a) Solve the following assignment problem to maximize production. The table shows the number of units produced
b) A decision problem has been expressed in the following pay off table:
What will be manager’s decision if he has: i) Maxi-Max Criterion ii) Maxi-Min Criterion iii) Mini-Max Regret Criterion iv) Hurwicz Criterion if coefficient of operation ( alpha – α ) is 0.7 v) Laplace Criterion. (10+5) |
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| 13. | Given the initial solution to the transportation problem test the optimality by Modified Distribution Method. If need be optimized.
Initial Solution:
From To Units Plant Project Transported W A 31 W B 25 X A 41 X C 41 Y B 77 |
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| 14. | Customers arrive at a booking office window being manned by a single individual at a rate of 25 per hour. The time required to serve the customer has an exponential distribution with a mean of 2 minutes. Find
i) Traffic Intensity ii) Idle time of the queuing system iii) Mean waiting time of the customer in the system and queue. iv) Average number of customers in the system and queue. v) Probability that the length of the queue is exactly 3.
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| 15. | Solve by Simplex Method
Maximize Z = 6x + 8y Subject to, 5x +10y≤ 60 4x +4y ≤ 40
Where x, y ≥ 0 |
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| SECTION – C | ||||||||||||||||||||||||||||||||||||||||||||||||||||
| III) | Case Study (1×20=20) | |||||||||||||||||||||||||||||||||||||||||||||||||||
| 16. | Dr. Suhan a dentist owns a Dental Clinic ‘Smile Innovators’. She schedules her patients for 20 minutes appointments. Some of the patients take more or less than 20 minutes depending on the type of dental work to be done. The following summary shows the various categories of work, their probabilities and the time actually needed to complete the work.
Simulate the dentist’s clinic for two hours and determine the average waiting time for the patients as well as the idleness of the doctor. Assume that all the patients show up at the clinic at exactly their scheduled arrival time starting at 6 p.m. Random numbers- 40, 82, 11, 34, 25, 66 |
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