Exploring Operations Research Concepts

What is the objective function in linear programming?

• The objective function in linear programming is a mathematical expression that defines the goal of the optimization problem.

• The objective function only applies to integer programming.

• The objective function is irrelevant to the optimization process.

• The objective function is always a constant value.

Define the feasible region in a linear programming problem.

• The feasible region is the set of all points that satisfy the constraints of a linear programming problem.

• The feasible region is the set of all possible solutions without any restrictions.

• The feasible region is the area where no constraints are met.

• The feasible region is the optimal solution to the problem.

What is the significance of the simplex method in linear programming?

• The simplex method is significant for efficiently solving linear programming problems to find optimal solutions.

• The simplex method is a graphical approach to linear programming.

• The simplex method is used to solve nonlinear equations.

• The simplex method is primarily for integer programming problems.

Explain the concept of duality in linear programming.

• Duality is the concept that linear programs can only have one optimal solution.

• In linear programming, duality is the principle that every linear program has an associated dual program, where the solutions to one provide insights into the solutions of the other.

• Duality refers to the ability to solve linear programs using only integer values.

• In linear programming, duality means that all variables must be positive.

What are the main components of a network flow problem?

• Source node, sink node, edges with capacities, flow conservation constraints.

• Source node, sink node, edges with capacities, flow direction constraints.

• Source node, sink node, edges with unlimited capacities, flow distribution rules.

• Source node, sink node, edges without capacities, flow optimization constraints.

How do you determine the maximum flow in a network?

• Use Dijkstra's algorithm to find the maximum flow.

• Calculate the minimum cut to determine the flow.

• Apply Kruskal's algorithm for maximum flow analysis.

• Use the Ford-Fulkerson method or Edmonds-Karp algorithm to find the maximum flow.

What is the purpose of the Ford-Fulkerson algorithm?

• To find the maximum flow in a flow network.

• To optimize the cost of transportation in logistics.

• To determine the minimum cut in a flow network.

• To calculate the shortest path in a graph.

Define a Nash equilibrium in game theory.

• A situation in a game where no player can benefit by changing their strategy while the other players keep theirs unchanged.

• A scenario where players can change their strategies freely without consequences.

• A state where all players must cooperate to achieve the best outcome.

• A situation where one player can always win regardless of others' strategies.

What is the difference between cooperative and non-cooperative games?

• Cooperative games allow binding agreements among players; non-cooperative games do not.

• Cooperative games are played in teams; non-cooperative games are played individually.

• Non-cooperative games allow binding agreements; cooperative games do not.

• Cooperative games involve random chance; non-cooperative games are purely strategic.

Explain the concept of zero-sum games.

• A zero-sum game is a scenario where players collaborate to achieve a common goal.

• A zero-sum game allows for mutual gains among players.

• A zero-sum game is a situation where one player's gain is equal to another player's loss, resulting in a net change of zero.

• In a zero-sum game, all players benefit equally regardless of the outcome.