Download AKTU B-Tech 1st Sem 2015-2016 EPL 051 Operation Research Question Paper

CA2076

EME-051/EPL-051

(Following Paper ID to be filled in your Answer Book)

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Paper ID : 140851/187851

Roll No.

B. Tech.

(SEM. I) THEORY EXAMINATION, 2015-16

OPERATION RESEARCH

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[Time: 3 hours]

[Total Marks : 100]

Note: Attempt all questions.

SECTION-A

1. Attempt any four of the following: [5x4=20]
   1. What is the main advantage of an OR model?

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   2. Describe the difference in standard form L.P.P. and canonical form L.P.P.
   3. Solve L.P.P. by graphical method :
      Max. Z = 8000X₁ + 7000 X₂
      Subject to constraints, 3X₁ + X₂ = 66
      X₁ + X₂ = 45
      

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      X₁ = 20
   4. A company has three departments with capacity 60, 50 and 80 units. The company manufactures products A, B, C and D. Profit per unit are 2, 3, 4 and 2 respectively. Products A, B, C and D need run time 2, 3, 2 and 4 in department 1. Product A, B, C and D need run time 3, 2, 2 and 1 in department 2. Product A, B, C and D need run time 2, 2, 1 and 2 in department 3. The total quantities are 40, 50, 30 and 40, and total run time of each department is 60 and 40 hours. Formulate L.P.P. to find maximize profit.
   5. Solve L.P.P. by Simplex method
      Max. Z = 3x₁ + 5x₂+4x₃
      Subject to:
      

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      2x₁ + 3x₂ = 8
      3x₁ + 2x₂ + 4x₃ = 15
      2x₂ + 5x₃ = 10 and
      X₁, X₂, X₃ = 0
   6. What are the essential characteristic of dynamic programming problem? State Bellman's principle of optimality.

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SECTION-B

2. Attempt any two of the following: (10x2=20)
   1. Explain any three techniques that are used in decision making under uncertainty.
   2. Find the range of values of p and q which will render the entry cell (2, 2) a saddle point from the game.

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3. Attempt any two of the following: (10x2=20)
   1. Find the optimum basic feasible solution by VAM in the following transportation problem.
      

      	W	X	Y	Z
      A	18	24	28	32
      B	8	13	17	18
      C	10	15	19	22

SECTION-C

4. Attempt any two of the following: (10x2=20)
   1. What is Economic Order Quantity ? Discuss any one, step by step, the development formula.

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   2. The demand for an item is deterministic and constant over the time and it is equal to 600 units per year. The per unit cost of item is Rs. 50 while the cost of placing an order is Rs. 5. The inventory carrying cost is 20% of the cost of inventory per annum and the cost of storage is Re. 1 per unit per month. Find the optimal ordinary quantity when stockouts are permitted. If the stock out are not permitted, what would be the loss to the company?
   3. Describe the simulation process. Write the different types of simulation languages.

SECTION-D

5. Attempt any two of the following: (10x2=20)
   1. What are the operating characteristics of a queuing model? Discuss the following terms:
      

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      (i) Balking
      (ii) Reneging
      (iii) Jockeying
   2. Draw a network diagram and determine the total free and independent floats and identity the critical path.
   
   

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   Activity:	0-1	1-2	1-3	2-4	2-5	3-4	3-6	4-7	5-7	6-7
   Duration:	2	8	10	6	3	3	7	5	2	8

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