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OPERATIONS RESEARCHUNIT - II Transportation problem is basically a (a) Maximization model (b) Minimization model (c) Transshipment problem (d) Iconic model The total number of allocation in a basic feasible solution of transportation problem of m × n size is equal to: (a) m × n (b) (m / n ) – 1 (c) ...

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OPERATIONS RESEARCH UNIT - II 1) Transportation problem is basically a (a) Maximization model (c) Transshipment problem

(b) Minimization model (d) Iconic model

2) The total number of allocation in a basic feasible solution of transportation problem of m × n size is equal to: (a) m × n (b) (m / n ) – 1 (c) m + n +1 (d) m + n – 1 3) In Northwest corner method the allocations are made (a) Starting from the left hand side top corner (b) Starting from the right hand side top corner (c) Starting from the lowest cost cell (d) Starting from the lowest requirement and satisfying first. 4) VAM stands for: (a) Value added method (c) Vogel Adam method

(b) Value assessment method (d) Vogel’s approximation method.

5) In the optimal solution, more than one empty cell have their opportunity cost as zero, it indicates (a) The solution is not optimal (b) The problem has alternate solution (c) Something wrong in the solution (d) the problem will cycle. 6) If ui and vj are row and column numbers respectively, then the implied cost is given by: (a) ui + vj (b) ui – vj (c) ui × vj (d) ui /vj 7) In a transportation problem where the demand or requirement is equal to the available resource is known as (a) Balanced transportation problem (b) Regular transportation problem, (c) Resource allocation transportation problem (d) Simple transportation model. 8) When the total allocations in a transportation model of m x n size is not equals to m + n – 1 the situation is known as (a) Unbalanced situation (b) Tie situation (c) Degeneracy (d) None of the above. 9) Assignment Problem is basically a (a) Maximization Problem (c) Transportation Problem

(b) Minimization Problem (d) Primal problem.

10) The Assignment Problem is solved by (a) Simplex method (c) Vector method

(b) Graphical method (d) Hungarian method.

11) The assignment matrix is always a (a) Rectangular matrix (c) Identity matrix

(b) Square matrix (d) None of the above

12) To balance the assignment matrix we have to: (a) Open a Dummy row (b) Open a Dummy column (c) Open either a dummy row or column depending on the situation (d) You cannot balance the assignment matrix 13) In cyclic traveling salesman problem the elements of diagonal from left top to right bottom are (a) Zeros (b) All negative elements (c) All infinity (d) all ones 14) To convert the assignment problem into a maximization problem (a) Deduct smallest element in the matrix from all other elements (b) All elements of the matrix are deducted form the highest element in the matrix (c) Deduct smallest element in any row from all other elements of the row (d) Deduct all elements of the row from highest element in that row 15) The similarity between Assignment Problem and Transportation Problem is: (a) Both are rectangular matrices (b) Both are square matrices (c) Both can be solved by graphical method (d) Both have objective function and non-negativity constraints 16) When the total supply is not equal to total demand in a transportation problem then it is called (a) Balanced (b) Unbalanced (c) Degenerate (d) None of these 17) Hungarian Method is used to solve (a) Transportation problem (c) A LP problem

(b) A travelling salesman problem (d) both a & b

18) The initial solution of a transportation problem can be obtained by applying any known method. However, the only condition is that (a) The solution is optimal (b) The rim conditions are satisfied (c) The solution not be degenerate (d) All of the above 19) The dummy source or destination in a transportation problem is added to (a) Satisfy rim conditions (b) Prevent solution from becoming degenerate (c) Ensure that total cost does not exceed a limit (d) None of the above 20) The occurrence of degeneracy while solving a transportation problem means that (a) Total supply equals total demand (b) The solution so obtained is not feasible (c) The few allocations become negative (d) none of the above 21) An alternative optimal solution to a minimization transportation problem exists whenever opportunity cost corresponding to unused route of transportation is: (a) Positive & greater than zero (b) Positive with at least one equal to zero (c) Negative with at least one equal to zero (d) none of the above 22) One disadvantage of using North-West Corner rule to find initial solution to the transportation problem is that (a) It is complicated to use (b) It does not take into account cost of transportation

(c) It leads to a degenerate initial solution

(d) All of the above

23) The solution to a transportation problem with ‘m’ rows (supplies) & ‘n’ columns (destination) is feasible if number of positive allocations are (a) m+n (b) m*n (c) m+n-1 (d) m+n+1 24) If an opportunity cost value is used for an unused cell to test optimality, it should be (a) Equal to zero (b) Most negative number (c) Most positive number (d)Any value 25) During an iteration while moving from one solution to the next, degeneracy may occur when (a) The closed path indicates a diagonal move (b) Two or more occupied cells are on the closed path but neither of them represents a corner of the path. (c) Two or more occupied cells on the closed path with minus sign are tied for lowest circled value (d) Either of the above 26) The large negative opportunity cost value in an unused cell in a transportation table is chosen to improve the current solution because (a) It represents per unit cost reduction (b) It represents per unit cost improvement (c) It ensure no rim requirement violation (d) none of the above 27) The smallest quantity is chosen at the corners of the closed path with negative sign to be assigned at unused cell because (a) It improve the total cost (b) It does not disturb rim conditions (c) It ensure feasible solution (d) all of the above 28) Which of the following methods is used to verify the optimality of the current solution of the transportation problem? (a) Least cost method (b) Vogel’s approximation method (c) Modified distribution method (d) All of the above 29) The degeneracy in the transportation problem indicates that (a) Dummy allocation(s) needs to be added (b) The problem has no feasible solution (c) The multiple optimal solution exist (d) a & b but not c 30) In a transportation problem, when the number of occupied routes is less than the number of rows plus the number of columns -1, we say that the solution is: (a) Unbalanced.

(b) Infeasible.

(c) Optimal.

(d) Degenerate

31) The only restriction we place on the initial solution of a transportation problem is that: we must have nonzero quantities in a majority of the boxes. (a) All constraints must be satisfied. (b) Demand must equal supply. (c) We must have a number (equal to the number of rows plus the number of columns minus one) of boxes which contain nonzero quantities. (d) None of the above

32) The initial solution of a transportation problem can be obtained by applying any known method. However, the only condition is that (a) The solution be optimal (b) the rim condition are satisfied (c) The solution not be degenerate (d) all of the above 33) The dummy source or destination in a transportation problem is added to (a) Satisfy rim condition (b) prevent solution from becoming degenerate (c) Ensure that total cost does not exceed a limit (d) all of the above 34) The occurrence of degeneracy while solving a transportation problem means that (a) Total supply equals total demand (b) the solution so obtained is not feasible (c) The few allocations become negative (d) none of the above 35) An alternative optimal solution to a minimization transportation problem exists whenever opportunity cost corresponding to unused routes of transportation is: (a) Positive and greater than zero (b) positive with at least one equal to zero (c) Negative with at least one equal to zero (d) all of the above 36) One disadvantage of using North-West Corner Rule to find initial solution to the transportation problem is that (a) It is complicated to use (b) it does not take into account cost of transportation (c) It leads to degenerate initial solution (d) all of the above 37) Dual of a Dual is (a) Primal (c) Prima dual

(b) Dual (d) none of the above

38) Primal of a Primal is : (a) Primal (c) Prima primal

(b) Dual (d) dual primal

39) Dual of a Dual of Dual is (a) Dual (c) Double dual

(b) Primal (d) Single dual

40) Primal of a dual is (a) Primal (c) Prime dual

(b) Dual (d) Prime primal

41) If Dual has a solution, then the primal will (a) Not have a solution (b) Have only basic feasible solution, (c) Have a solution (d) none of the above. 42) If Primal Problem is a maximization problem, then the dual will be (a) Maximization Problem (b) Minimization Problem (c) Mixed Problem (d) None of the above...