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Week 4 quiz

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Question;1.Decision variables in network flow problems;are represented by;a) arcs;b) nodes;c) demands;d) supplies;2. A node which can both send to and receive;from other nodes is a;a) transshipment;node;b) demand;node;c) random;node;d) supply;node;3.The problem which deals with the;distribution of goods from several sources to several destinations is the;a) assignment;problem;b) maximal;flow problem;c) shortest-route;problem;d) transportation;problem;4. The assignment problem is a special case;of the;a) transportation;problem;b) transshipment;problem;c) maximal;flow problem;d) shortest-route;problem;5. The objective of the transportation;problem is to;a) Minimize;the cost of shipping products from several origins to several destinations.;b) Minimize;the total number of origins to satisfy total demand at the destinations.;c) Minimize;the number of shipments necessary to satisfy total demand at destination.;d) Identify;one origin that can satisfy total demand at the destinations and at the same;time minimize total shipping costs.;6. The parts of a network that represent the;origins are;a) the;capacities;b) the;flows;c) the;nodes;d) the;arcs;7. Arcs in the transshipment problem;a) must;connect every node to the transshipment node;b) represent;the cost of shipments;c) indicate;the direction of flow;d) All;of the alternatives are correct;8. If the transportation problem has 4;origins and 5 destinations, the LP formulation of the problem will have;a) 18;constraints;b) 5;constraints;c) 20;d) 9;9. Maximal flow problem differs from the;other network models in which way;a) Arcs;have unlimited capacity;b) Multiple;supply nodes are usual;c) Arcs;have limited capacity;d) Arcs;are two directions;10. Maximal flow problem are converted to;transshipment problems by;a) Adding;extra supply nodes;b) Adding;supply limits on supply nodes;c) requiring;integer solutions;d) Connecting;the supply and demand nodes with the return arc;11. The objective value function for the ILP;problem can never;a) Be;better than the optimal solution to its LP relaxation;b) Be;as poor as the optimal solution to its LP relaxation;c) Be;as good as theoptimal solution to its LP relaxation;d) Be;as worse than the optimal solution to its LP relaxation;12. For minimization problems, the optimal;objective function value to the LP relaxation provides what for the optimal;objective function value of the ILP problem.;a) An;additional constraint for the ILP;b) An;upper bound;c) An;alternative optimal solution;d) A;lower bound;13. In the model X1 >= 0 and integer, X2;= 0, and X3>= 0,1. (All the numbers in the question answers are small;and in the lower right corner of the X);a) X1=2;X2=3, X3=.578;b) X1=;5, X2=3, X3= 0;c).X1=0;X2= 8, X3= 0;d) X1=4;X2= 389, X3=1.;14. Rounding the solution of an LP relaxation;integer to the nearest integer value provides;a) An;infeasible solution;b) An;integer solution that might neither be feasible nor optimal;c) A;feasible but not necessarily optimal integer;d) An;integer solution that is optimal.;15. The solution the LP relaxation of a;maximization integer linear programming involves;a) An;upper bound for the value of an objective function;b) A;lower bound for the value of an objective function;c) An;upper bound for the value of a decision variables;d) A;lower bound for the value of a decision variable;16. Sensitivity analysis for the integer;linear programming;a) Can;be provided only by computer;b) Does;not have the same interpretation and should be disregarded;c) Has;precisely the same interpretation as that from linear programming;d) Is;most useful for 0-1 models;17. Let X1, X2, and X3 be 0-1 variables whose;values indicates whether the projects are not done (0) or are done (1). Which;answer below indicates that at least two of the projects? (All the numbers in;the question answers are small and in the lower right corner of the X);a) X1-X2=0;b) X1+X2+X3=2;c) X1+X2+X3 =2;18. In an all-integer linear program;a) All;objective functions coefficients must be integer;b) All;objective functions coefficients and right hand side value must be integer;c) All;variables must be integer;d) All;right hand side values must be integer;19. How is an LP problem change into an ILP;problem?;a) By;adding constraints that the decision variables be non-negative;b) By;adding integrality conditions;c) By;making right hand side value integer;d) By;adding discontinuity constraints;20. The constraint X1+X2+X3+X4

Paper#37011 | Written in 18-Jul-2015

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