Download JNTUH MCA 2nd Sem R09 2017 August F3204 Operations Research Question Paper

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Code No: F3204 R09

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JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

MCA I Semester Examinations, August - 2017

OPERATIONS RESEARCH

Time: 3hrs Max.Marks:60

Answer any five questions

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All questions carry equal marks

1. a) Solve the LPP by Graphical method
   Maximize z=3x+5y
   Such that
   x+3y < 25, 3x+2y < 50
   

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   5x-3y<10, x,y>0
   
   b) Write about the Phases of Operations research. [6+6]
2. Solve the following LPP by simplex method.
   Maximize z = 6x₁ —2x₂ +3x₃ subject to [12]
   

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   2x₁ —x₂ +2x₃<2
   x₁ +4x₂ <4
   x₁, x₂,x₃ = 0
3. Solve the following the transportation problem. [12]
   

   	D1	D2	D3	D4	D5	Supply
   O1	3	4	6	8	9	20
   O2	2	10	1	5	8	30
   O3	7	11	20	40	3	15
   O4	2	1	9	14	16	13
   Demand	40	6	8	18	6	Total 78

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4. a) Formulate assignment model problem mathematically.
   b) Explain Hungarian method for optimal solution with an example. [6+6]
5. Obtain the optimum sequencing by using Johnson’s Rule.
   There are 5 jobs, each of which must go through the machines A,B, and C in the
   order ABC Jobs Also find the total elapsed time T and the idle time on each
   

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   machine. [12]
   
   

   Processing time A	5	7	6	9	5
   Processing time B	2	1	4	5	3
   Processing time C	3	7	5	6	7

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7. a) A truck owner finds from his past records that the maintenance costs per year of a
   truck whose purchase price is Rs 8000 are given below
   
   

   Year	1	2	3	4	5	6	7	8
   Maintenance cost (Rs)	1000	1300	1700	2200	2900	3800	4800	6000
   Resale price ( Sr)	4000	2000	1200	600	500	400	400	400

   Determine at which time it is profitable to be replaced. [12]
   b) Two players A and B match the coins. If the coins match A wins 1 unit of value.
   

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   If coins do not match B wins 1 unit of value. Determine the pay off matrix, the
   best strategies for each player and the value of the game.
8. Solve the following game by Dominance method. [6+6]
   

   4	4	12	-4	-6
   8	6	8	-4	0
   10	2	4	10	12

9. A stockist has to supply 400 units of a product every Monday to his customers.
   

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   He gets the product at Rs.50 per unit from the manufacturer. The cost of ordering
   and transportation from the manufacturer is Rs.75 per order. The cost of carrying
   inventory is 7.5% per year of the cost of the product.
   Find:
   a) The economic lot size.
   

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   b) The total optimal cost (including the capital cost). [6+6]

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