Operations Research-1

 

GAYATRI VIDYA PARISHAD COLLEGE FOR DEGREE & P.G COURSES (A)

III Year B.Sc. (STATISTICS)

Semester – V, STATISTICS : MODEL PAPER

Paper-VI(A): Operation Research 1

(With effect from 2020-21AB)

Date:                                                                                       Max. Marks: 75

TIME:

SECTION-A

  I. Answer the following questions                                                   5× 10 = 50 M

 

1.       (a). Explain the Nature and Features Of Operation Research. (CO1)

(OR)

              (b). Solve the Following LPP by Graphical Method. (CO2)

                                 Minimize (z) = 20x+10y

                                 Subject to constraints:    x+2y≤40

                                    3x+y≥30

                                   4x+3y≥60 and x, y≥0

 

2.       (a). State and Prove Fundamental Theorem Of LPP

(OR)

            (b). Use Simplex Method to Solve the Following Linear Programming Problem. (CO3)

                                           Max(z)=3x₁+5x₂+4x₃

                                               Subject to constraints:    2x₁+3x₂≤8

                                                   2x₂+5x₃≤10

                                                  3x₁+2x₂+4x₃≤15 and x₁,x₂,x₃≥0

                                                                            

3.        (a). Use the Penalty Method To Solve The Following LP Problem.(CO3)

Min(z)=5x₁+3x₂

                          Subject to constraints: 2x₁+4x₂≤12

2x₁+2x₂=10

5x₁+2x₂≥10 and x₁,x₂≥0

 

(OR)

             (b) Use Two-Phase Simplex Method to Solve the LPP.(CO3)

Max(z)=5x₁-4x₂+3x₃

                   Subject to constraints: 2x₁+x₂-6x₃=20

           6x₁+5x₂+10x₃≤76

8x₁-3x₂+6x₃≤50 and     x₁,x₂,x₃≥0

 

4.       (a)  Solve the following LPP using Duality

                       Maximize (z) = 6x+8y

                          Subject to constraints:   5 x+2y≤20

                              x+2y≤10

                                x, y≥0

(OR)

            (b) Use the Dual Simplex Method to Solve the LPP. (CO3)

                        Max(z) =-3x₁-2x₂

                          Subject to constraints:    x₁+x₂≥1

                  x₁+x₂≤7

                  x₁+2x₂≥10

                  x₂ ≤3 and x₁,x₂≥0

.

5.       (a) Explain Maximin and Minimax priciple in Game theory.

(OR)

         (b) Solve the Following Pay-off matrix. Also determine the optimal     

                 strategies and the value of the games.

                                                   B

                                              5        1

                                    A       3        4

                                                           SECTION-B

II. Answer the following five questions.                                                       5×3=15M

6. Explain the Scope of Operation Research

7. Write the Limitations of Operations Research.

8. Explain the Concept of Degeneracy of LPP.

9. Prove that the Dual of Dual is Primal LPP

10. Explain the Artificial Variable Techniques.                          

11. Explain General Form of LPP.   

12. Explain Un restricted variable and Unbounded Solution.

13. Explain Pure Strategy and Mixed Strategy.

 

SECTION-C

III. Answer all the following questions.                                                   5×2=10M

14. Define Convex Set.

15. Define Unbounded Solution.

16. What is Artificial Variable?

17. What is Primal Dual Pairs in Matrix Form?      

18. Define Two-Person zero-sum game.