Download JNTUH MCA 2nd Sem R13 2018 June-July 812AK Operations Research Question Paper

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Code No: 812AK R13

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JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

MCA I Semester Examinations, June/July- 2018

OPERATIONS RESEARCH

Time: 3 Hours Max. Marks: 60

Note: This question paper contains two parts A and B.

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Part A is compulsory which carries 20 marks. Answer all questions in Part A. Part B consists of 5 Units. Answer any one full question from each unit. Each question carries 8 marks and may have a, b, c as sub questions.

PART - A 5 x 4 Marks =20

1. Explain the structure of linear programming problems (LPPs) with an example. [4]
2. Give the applications of transportation problem in industries. [4]
3. Distinguish between gradual failures and sudden failures and their effects. [4]

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4. Explain the relevance of game theory to managerial problems. [4]
5. What is selective inventory control? Why do you optimize this in large industries? [4]

PART -B 5 x 8 Marks =40

1. a) Use the two-phase simplex method to:
   Minimize Z = 5x₁ + 6x₂
   

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   Subject to:
   x₁ + x₂ = 5
   3x₁ + x₂ = 10
   x₁ + 3x₂ = 6
   and x₁, x₂ = 0 [8]
   

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   OR
   b) An animal feed company must produce 200 kg of a mixture consisting of ingredients X₁ and X₂ daily. X₁ costs Rs. 3 per kg and X₂ costs Rs. 8 per kg. Not more than 80 kg of X₁ can be used and at least 60 kg of X₂ must be used. Find how much of each ingredient should be used if the company wants to minimize the cost? Formulate the above problem and solve it by the simplex method. [8]
2. a) What is the difference between a transportation problem and an assignment problem? When does degeneracy occur in a transportation problem? [4+4]
   OR
   b) There are five jobs to be assigned to 5 machines and the associated cost matrix is as follows:
   

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   Jobs	I	II	III	IV	V
   A	11	17	8	16	20
   B	9	7	12	6	15
   C	13	16	15	12	16
   D	21	24	17	28	26
   E	14	10	12	11	15

   
   Find the optimum assignment and the associated cost using the assignment technique. [8]
3. a) There are six jobs, each of which must go through machines A, B and C. Processing time (in hours) is given in the following table. Find the sequence that minimizes the total elapsed time required to complete the following tasks [8]
   

   Job	1	2	3	4	5	6
   Machine A	12	10	9	14	7	9
   Machine B	7	6	6	5	4	4
   Machine C	6	5	6	4	2	4

   
   OR
   

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   b) 1000 bulbs are in use and it costs Rs 10 to replace an individual bulb which has burnt out. If all bulbs were replaced simultaneously it would cost Rs 4 per bulb. It is proposed to replace all bulbs at fixed intervals of time, whether or not they have burnt out and to continue replacing burnt out bulbs as and when they fail. The failure rates have been observed for a certain type of light bulb as follows:
   

   Week	1	2	3	4	5
   Percent failing by the end of week	10	25	50	80	100

   
   At what intervals should all the bulbs be replaced? At what group replacement price per bulb would a policy of strictly individual replacement become preferable to the adopted policy? [8]
4. a) Find the longest path between the towns A and E using the dynamic programming approach. [8]
   OR
   

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   b) A company management and the labor union are negotiating a new three-year settlement. Each of these has four strategies:
   I: Hard and aggressive bargaining.
   II: Reasoning and logical.
   III: Legalistic strategy.
   IV: Conciliatory approach.
   

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   The costs to the company are given for every pair of strategy choice.
   Company strategies

   	I	II	III	IV
   Union strategies I	20	15	12	35
   II	25	14	8	10
   III	40	2	10	5
   IV	-5	4	11	0

   What strategy will the two sides adopt? Also, determine the value of the game. Use the minimax - maximin rule and then verify your result with the dominance rule. [8]
5. a) Monthly demand for an item is 200 units. Ordering cost is Rs. 350, inventory carrying charge is 24% of the purchase price per year. The purchase prices are P₁ = Rs. 10 for purchasing Q₁ = 500; P₂ = Rs. 9.25 for purchasing 500 < Q₂ < 750 and P₃ = Rs. 8.75 for purchasing 750 < Q₃. Determine the optimum purchase quantity. If the order cost is reduced to Rs. 100 per order, compute the optimum purchase quantity. [8]
   OR
   b) Customers arrive at a box office window being managed by a single individual according to a Poisson input process with a mean rate of 30 per hour. The time required to serve a customer has an exponential distribution with a mean of 90 seconds. Find the average waiting time of a customer. Also, determine the average number of customers in the system and the average queue length. [8]

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