Download PTU B.Tech 2020 March CSE-IT 6th Sem IT 310 Operation Research Question Paper

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Roll No. [ TTTTTT] Total No. of Pages : 02

Total No. of Questions : 18

B.Tech.(CSE) (O.E. 2012 to 2017) (Sem.-6)

OPERATION RESEARCH

Subject Code : IT-310

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M.Code : 71554

Time : 3 Hrs. Max. Marks : 60

INSTRUCTIONS TO CANDIDATES :

1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks each.
2. SECTION-B contains FIVE questions carrying FIVE marks each and students have to attempt any FOUR questions.

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3. SECTION-C contains THREE questions carrying TEN marks each and students have to attempt any TWO questions.

SECTION-A

Explain the following :

1. Artificial Variable
2. Initial Feasible solution

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3. Unbalanced transportation problem
4. Least cost method
5. Minimum spanning tree problem
6. Relation between dual and primal
7. Dummy event

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8. Payoff matrix
9. Mathematical formulation of the LPP
10. Saddle point

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SECTION-B

11. Use Big M method to solve : Maximize Z = x + y subject to constraints : 2x + y > 4, x+7y>=7,x>=0,y>=0.

12. Write differences between PERT and CPM.

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13. Solve the travelling salesman problem so as to minimize the cost per cycle C_ij = 20, C₁₃ = 4, C₁₄ = 10, C₂₃ = 5, C₃₄ = 6, C₂₅ = 10, C₃₅ = 6, C₄₅ = 20, where C_ij = C_ji and there is no route between cities if a value C_ij is not shown.

14. Consider a transportation Problem with m = 3 and n = 4 where. C₁₁=2, C₁₂=3, C₁₃=11, C₁₄=7, C₂₁=1, C₂₂=0, C₂₃=6, C₂₄=1, C₃₁=5, C₃₂=8, C₃₃ = 15, C₃₄=9 Suppose S₁ = 6, S₂ = 1, S₃ = 10, whereas D₁ = 7, D₂ = 5, D₃ = 3, D₄ = 2. Use Least cost method to find its solution.

15. State and prove Maximin-Minimax Principle for the selection of the optimal strategies by the two players, with example.

SECTION-C

16. Use Branch and bound method to solve : Maximize Z = 7x + 9y subject to constraints : —x+3y<=6, 7x+y <=35 y<=7;x>=0, y>=0 and are integers.

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17. Explain {(M/M/1):(N/FIFO)} system and solve it under steady state conditions.

18. Use Simplex method to solve the goal programming problem : Minimize Z = Pd₁ +5Pd₂ +3Pd₃ + P₁d₄ + P₁d₅ subject to constraints : X₁ +x₂+d₁ —d₂ =80, X₁ +x₂+d₃ —d₄ =90, x₁+d₅ =70, x₂ +d₆ =45, x₁,x₂,d₁, d₂,d₃,d₄,d₅,d₆ >=0

NOTE : Disclosure of Identity by writing Mobile No. or Making of passing request on any page of Answer Sheet will lead to UMC against the Student.

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