Operational research B.C.A 17-20 SEM 4, Sec Internal March 2019

SAINTGITS COLLEGE OF APPLIED SCIENCES

SECOND INTERNAL ASSESSMENT EXAMINATION, March2019

Department of BCA, Semester 4

Operational Research

Total   : 80 marks                                                                        Time:3Hours

Section A

1.Sum of supply not equal to sum of demand

2.Solution which satisfies the objective function.

3.Set of values of the variables which satisfy all the constraints and non negative restrictions of the problem.

4.Min z=, ,

5.Number of allocation is less than m+n-1

6.Position in the pay off matrix where the maximin coincides with minimax

7.2

8.If the algebraic sum of the outcomes of all players together is zero.

9.In L.P.P constraints are ≥ type we add surplus variable to make equality.

10.Assign a number of persons to equal number of destination at minimum cost.

11.Number of rows not equal to number of columns. In this case we introduce dummy rows or columns.

12.In a L.P.P if there are m variables and n constraints .If m>n , then we put zero values for m-n variables . These n variables are called basic and m-n variables are called non basic variables.                                         

                     Section B

13.6

14.Draw graph x=.75, y=3.5 z=19.75

                X=.8,y=3.6 z=20.4

                X=4, y=6 , z= 42

                X=4, y=2, z= 22

                X=2,  y=2, z=19 is the solution

15.A-I 6 units, B-I 1 unit

16. Transportation Problem-Subclass of linear programming problem, Number of origins need not be equal to number of destination. Unbalanced if sum of supply not equal to sum of demand. Here a positive quantity is allocated from a source to destination.

    Assignment problem –Special type of transportation problem, Number of rows and columns are equal. unbalanced if number of rows and columns are not equal. Here a job is assigned to a destination.

17.first table key element 1, second table key element-5, x= ,y=   , z=18

18.(1) There are finite number of players(2)Each player has a finite number of course of action(3)Every play is associated with an outcome known as pay off(4) A  play is said to be played when each of the players choose a single course of action.

19.After the initial basic feasible solution form m=n-1 equations of the form u_i+v_j=c_ij corresponding to each occupied cell. For solving the equations , take one of u_i or v_j as zero. Calculate d_ij=c_ij-(u_i+v_ij)If all  d_ij≥0, the solution is optimal.

20.The principle of dominance states that if the strategy of a player dominates over another in all conditions, then the latter can be ignored.

21.111

                                                                (6x5=30)

         

Section C.

22.A-1, B-2, c-3, D-4

        A-1, B-3, C-2, D-4, cost=50

23. First table key element=8-2M, second table key element=3-M, third table key element—M+8, x=80, y=120, z=1200

24. In a game ,if the algebraic sum of the outcomes of all the players together is zero, the game is called zero sum game. Otherwise non zero sum game. Using dominance principle solve the problem .

25. Using vogel’s method find the initial basic solution and then solve.