39 real Operations Research questions from the Mechanical Core bank, as asked in Indian campus drives and tech interviews. Every question has a verified answer and an AI-tutor explanation on placd — free to start.
1. What is Linear programming problem?
Junior
A.the convex set of all points satisfying every constraint, whose corner points are the only candidates for a linear optimum
B.a non-negative quantity added to a less-than-or-equal constraint to turn it into an equality for the simplex tableau
C.an optimisation of a linear objective function subject to linear equality and inequality constraints on non-negative decision variables
D.the time an activity can be delayed without delaying project completion, being zero for every activity on the critical path
2. Which term means: "an optimisation of a linear objective function subject to linear equality and inequality constraints on non-negative decision variables"?
A.Linear programming problem — the time an activity can be delayed without delaying project completion, being zero for every activity on the critical path
B.Linear programming problem — an optimisation of a linear objective function subject to linear equality and inequality constraints on non-negative decision variables
C.Linear programming problem — a probabilistic network method that derives each activity's expected duration from optimistic, most likely and pessimistic estimates using a beta-distribution weighting
D.Linear programming problem — a special transportation problem in which each of n jobs must be given to exactly one of n agents at minimum total cost
A.Feasible region — the convex set of all points satisfying every constraint, whose corner points are the only candidates for a linear optimum
B.Feasible region — an initial-solution rule for transportation problems that allocates along the row or column with the largest penalty between its two cheapest routes
C.Feasible region — a probabilistic network method that derives each activity's expected duration from optimistic, most likely and pessimistic estimates using a beta-distribution weighting
D.Feasible region — an optimisation of a linear objective function subject to linear equality and inequality constraints on non-negative decision variables
A.the row- and column-reduction algorithm that solves an assignment problem by creating enough zeros to cover all assignments with n lines
B.an iterative procedure that moves from one corner point of the feasible region to an adjacent better one until no improving direction remains
C.a special transportation problem in which each of n jobs must be given to exactly one of n agents at minimum total cost
D.the condition in which a basic variable takes the value zero, which can stall the simplex method by allowing iterations that do not improve the objective
8. Which term means: "an iterative procedure that moves from one corner point of the feasible region to an adjacent better one until no improving direction remains"?
A.Simplex method — an iterative procedure that moves from one corner point of the feasible region to an adjacent better one until no improving direction remains
B.Simplex method — a non-negative quantity added to a less-than-or-equal constraint to turn it into an equality for the simplex tableau
C.Simplex method — a distribution problem in which total supply equals total demand, so no dummy source or destination is needed before solving
D.Simplex method — an optimisation of a linear objective function subject to linear equality and inequality constraints on non-negative decision variables
A.Slack variable — a distribution problem in which total supply equals total demand, so no dummy source or destination is needed before solving
B.Slack variable — the correspondence by which every maximisation problem has an associated minimisation problem whose optimal objective value is identical
C.Slack variable — the row- and column-reduction algorithm that solves an assignment problem by creating enough zeros to cover all assignments with n lines
D.Slack variable — a non-negative quantity added to a less-than-or-equal constraint to turn it into an equality for the simplex tableau
A.an optimisation of a linear objective function subject to linear equality and inequality constraints on non-negative decision variables
B.a probabilistic network method that derives each activity's expected duration from optimistic, most likely and pessimistic estimates using a beta-distribution weighting
C.the correspondence by which every maximisation problem has an associated minimisation problem whose optimal objective value is identical
D.the condition in which a basic variable takes the value zero, which can stall the simplex method by allowing iterations that do not improve the objective
14. Which term means: "the condition in which a basic variable takes the value zero, which can stall the simplex method by allowing iterations that do not improve the objective"?
A.Degeneracy in linear programming — a special transportation problem in which each of n jobs must be given to exactly one of n agents at minimum total cost
B.Degeneracy in linear programming — the time an activity can be delayed without delaying project completion, being zero for every activity on the critical path
C.Degeneracy in linear programming — the condition in which a basic variable takes the value zero, which can stall the simplex method by allowing iterations that do not improve the objective
D.Degeneracy in linear programming — an iterative procedure that moves from one corner point of the feasible region to an adjacent better one until no improving direction remains
17. Which term means: "the correspondence by which every maximisation problem has an associated minimisation problem whose optimal objective value is identical"?
A.Duality in linear programming — a non-negative quantity added to a less-than-or-equal constraint to turn it into an equality for the simplex tableau
B.Duality in linear programming — a distribution problem in which total supply equals total demand, so no dummy source or destination is needed before solving
C.Duality in linear programming — the row- and column-reduction algorithm that solves an assignment problem by creating enough zeros to cover all assignments with n lines
D.Duality in linear programming — the correspondence by which every maximisation problem has an associated minimisation problem whose optimal objective value is identical
A.a distribution problem in which total supply equals total demand, so no dummy source or destination is needed before solving
B.a non-negative quantity added to a less-than-or-equal constraint to turn it into an equality for the simplex tableau
C.the condition in which a basic variable takes the value zero, which can stall the simplex method by allowing iterations that do not improve the objective
D.the row- and column-reduction algorithm that solves an assignment problem by creating enough zeros to cover all assignments with n lines
A.Balanced transportation problem — the time an activity can be delayed without delaying project completion, being zero for every activity on the critical path
B.Balanced transportation problem — the condition in which a basic variable takes the value zero, which can stall the simplex method by allowing iterations that do not improve the objective
C.Balanced transportation problem — deliberately shortening activity durations at extra cost, applied to critical activities in order of least cost slope to compress the project
D.Balanced transportation problem — a distribution problem in which total supply equals total demand, so no dummy source or destination is needed before solving
23. Which term means: "an initial-solution rule for transportation problems that allocates along the row or column with the largest penalty between its two cheapest routes"?
A.Vogel's approximation method — the correspondence by which every maximisation problem has an associated minimisation problem whose optimal objective value is identical
B.Vogel's approximation method — the condition in which a basic variable takes the value zero, which can stall the simplex method by allowing iterations that do not improve the objective
C.Vogel's approximation method — a special transportation problem in which each of n jobs must be given to exactly one of n agents at minimum total cost
D.Vogel's approximation method — an initial-solution rule for transportation problems that allocates along the row or column with the largest penalty between its two cheapest routes
A.Assignment problem — the row- and column-reduction algorithm that solves an assignment problem by creating enough zeros to cover all assignments with n lines
B.Assignment problem — a special transportation problem in which each of n jobs must be given to exactly one of n agents at minimum total cost
C.Assignment problem — the correspondence by which every maximisation problem has an associated minimisation problem whose optimal objective value is identical
D.Assignment problem — a probabilistic network method that derives each activity's expected duration from optimistic, most likely and pessimistic estimates using a beta-distribution weighting
A.an initial-solution rule for transportation problems that allocates along the row or column with the largest penalty between its two cheapest routes
B.a special transportation problem in which each of n jobs must be given to exactly one of n agents at minimum total cost
C.the condition in which a basic variable takes the value zero, which can stall the simplex method by allowing iterations that do not improve the objective
D.the row- and column-reduction algorithm that solves an assignment problem by creating enough zeros to cover all assignments with n lines
29. Which term means: "the row- and column-reduction algorithm that solves an assignment problem by creating enough zeros to cover all assignments with n lines"?
A.Hungarian method — the correspondence by which every maximisation problem has an associated minimisation problem whose optimal objective value is identical
B.Hungarian method — a probabilistic network method that derives each activity's expected duration from optimistic, most likely and pessimistic estimates using a beta-distribution weighting
C.Hungarian method — a distribution problem in which total supply equals total demand, so no dummy source or destination is needed before solving
D.Hungarian method — the row- and column-reduction algorithm that solves an assignment problem by creating enough zeros to cover all assignments with n lines
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