ST. JOSEPH’S COLLEGE OF COMMERCE (AUTONOMOUS) |
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| END SEMESTER EXAMINATION – MARCH/APRIL 2016 | ||||||||||||||||||||||||||||||||||||
| M.COM(I.B.) – II SEMESTER | ||||||||||||||||||||||||||||||||||||
| P4 15 AR 201: OPERATION 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. | Three products are processed through three different operations. The times (in minutes) required per unit for each product, the daily capacity of the operations (in minutes per day) and the profit per unit sold for each product (in rupees) are as follows:
The zero time indicates that the product does not require the given operation. It is assumed that all units produced are sold. Moreover, the given profits per unit are net values that result after all pertinent expenses are deducted. The problem is to determine the optimum daily production for three products that maximizes the profit. Formulate the above production planning problem in a linear programming problem. |
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| 2. | Find the dual of the following problem:
Maximize Z = 6x1+8x2 Subject to 2x1 + 3x2 ≤ 16 4 x1 + 2x2 ≥ 16 2x1 + x2 = 16 x1 , x2 ≥ 0
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| 3. | A director in a Management Institute has the problem of assigning courses to teachers with a view to maximizing educational quality in his Institute. He has available to him one professor, two associate professors, and one teaching assistance (TA). Four courses must be cleared and, after appropriate evaluation, has arrived at the following relative ratings regarding the ability of each instructor to teach each of the four courses
How should he assign his staff to the courses to realize his objective?
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| 4. | At Dr. Prachi’s clinic patients arrive at an average of 6 patients per hour. The clinic is attended to by Dr. Prachi herself. The doctor takes 6 minute per patient to serve them. It can be assumed that arrivals follow a Poisson distribution and the doctor’s inspection time follows an exponential distribution. Determine:
i) The percent of time a patient can walk right inside the doctor’s cabin without having to wait.(Traffic Intensity) ii) The average no. of patients in Dr. Prachi clinic. iii) The average no. of patients waiting for their turn. iv) The average time a patients spends in the clinic.
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| 5. | Plot separately the following equations in a Graph. Also highlight the feasible area in each case.
i) 4x + 6y ≤ 12 ii) 4x + 6y ≥ 12 iii) 4x + 6y = 12
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| 6. | A project consists of the following activities with the time estimates noted against each:
Required: i) Draw a network diagram. ii) Determine the critical path and its duration.
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| 7. | Baroda lather shop has three manufacturing plants and four sales outlets. Data of daily demand at various sales outlets and supply from various plants along with transportation cost per unit between plants and sales outlets are given in the following table. Determine the Initial Basic Feasible Solution (IBFS) by using the Least Cost Method
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| 8. | A company’s management and labour union are negotiating a new three years settlement. Each party has four strategies these are:-
I. Hard and aggressive bargaining approach. II. Reasoning and logical Approach
III. Legalistic approach IV. Conciliatory Approach The cost to the company for every pair of strategy choices are given in the table below:
Which strategy should the management adopt and which strategy should the union adopt? Solve and find the value of the game through the Maximin Minimax principle.
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| 9. | Sofitel Plumbing and Heating maintains a stock of 30 –gallon hot water heaters that is sells to homeowners and installs for them. Owner Mr. Gupta likes the idea of having a large supply on hand to meet customer demand, but he also recognizes that it is expensive to do so. He examines hot water heater sales over the past 50 weeks and notes the following.
a) Simulate the data and determine the average number of sales per week over a 6- week period? Random Numbers: 10, 24, 03, 32, 23, 59.
b) If Mr. Gupta maintains a constant supply of 8 hot water heaters in any given week, calculate the closing stock at the end of the 6-week period?
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| 10. | “Operation Research is concerned with scientifically deciding how best to design and operate man machine systems usually under conditions requiring the allocation of scare resources. In light of this statement explain the main features of Operation Research.
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| SECTION – B | ||||||||||||||||||||||||||||||||||||
| II. | Answer any THREE questions. Each carries 15 marks. (3×15=45) | |||||||||||||||||||||||||||||||||||
| 11. | Two caters, A & Co. and B & Co. are competing for an increased market share. The payoff matrix, shown in the following table, describes the increase in market share for A & Co. and decrease in market share of B & Co.
B & Company
i) Determine optimal strategies for both the manufactures and the value of game by using the Dominance method. ii) Determine the probability of company A and B choosing each strategy. |
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| 12. | i) Obtain an IBFS to the following transportation problem by VAM.
ii) Is the solution degenerate? Test the optimality of the solution thus Obtained using the MODI method. If not, optimize the solution.
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| 13. | A city corporation has decided to carry out road repairs on main four entries of the city. The govt. has agreed to make a special grant of Rs.106 lakhs towards the cost with a condition that the repairs must be done at the lowest cost & quickest time. If conditions warrant, then supplementary grants will also be considered favorable. The corporation has floated tenders and 5 contractors have sent in their bids (in lakhs). In order to expedite work, one road will be awarded to only one contractor:
i) Find the best way of assigning the repair work to the contractors to reduce the costs. ii) If it is necessary to seek supplementary grants, then what should be the amount sought? iii) Which of the five contractors will be unsuccessful in his bid? |
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| 14. | A single counter Ticket Booking Centre employs one Booking Clerk. A Passenger on arrival immediately goes to the Booking Counter for being served if the Counter is free. If, on the other hand, the Counter is engaged, the Passenger will have to wait. The Passengers are served on first come first served basis. The time of arrival and the time of service varies from 1 minute to 6 minutes. The distribution of arrival and services time is as under:
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| 15. | Solve by Simplex method the model given below
Max Z = 22x1 + 18 x2
Subject to constraints x1 +x2 ≤ 20 360x1 + 240x2 ≤ 5760 Where x1 , x2 ≥ 0 |
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| SECTION – C | ||||||||||||||||||||||||||||||||||||
| III. | Case Study (1×20=20) | |||||||||||||||||||||||||||||||||||
| 16. | A small project consists of seven activities, whose time estimates are given in the following:
a) Determine the expected time and variance for each activity. b) Draw the network and determine the project duration and critical path. c) Determine the total float, free float and independent float for each activity. d) What is the probability that the project is completed 4 days earlier than expected? e) What is the probability that the project is completed 4 days later than expected?
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