Test on Operations Research: Theory and Applications

Question 1: The B-inverse matrix is identified as an essential component of an LP model.

A. Ano

B. Ne

Explanation: The essential components of an LP model are decision variables, objective function, constraints, parameters/coefficient values, and non-negativity restrictions. The B-inverse matrix is not listed among these components.

Question 2: Which of the following statements accurately describe the construction of an LP model for production planning, according to the study materials?

A. The decision variables typically represent the production quantities.

B. The objective is to minimize total production cost or maximize total profit.

C. Constraints commonly include limits on machine hours, labor hours, and material availability.

D. Constraints commonly include minimum/maximum calorie intake or budget for food items.

Explanation: For production planning, the variables are production quantities. The objective is to maximize total profit or minimize total production cost. Typical constraints include resource limits like machine hours, labor hours, material availability, storage capacity, and demand limits. Constraints related to calorie intake or food budgets are typical for diet problems, not production planning.

Question 3: The primary objective of the Maximum Flow Problem is to identify the path with the smallest capacity from a source to a sink.

A. Ano

B. Ne

Explanation: The study materials state that the main goal of the Maximum Flow Problem is to "Send the largest possible flow from a source to a sink through a network with capacity limits," not to find the path with the smallest capacity.

Question 4: Edge weights in a weighted graph can represent distance in routing, time in scheduling, cost in transportation, or capacity in flow networks.

A. Ano

B. Ne

Explanation: Weights in a graph can be interpreted as distance in routing, time in scheduling, cost in transportation, or capacity in flow networks.

Question 5: Which of the following describes a step in Dijkstra's algorithm for the shortest path problem, according to the study materials?

A. It starts by setting the source node's distance to 0.

B. It identifies the longest path from the source to all other nodes.

C. It repeatedly selects the visited node with the largest distance to relax its edges.

D. It ensures that all edges are duplicated to create an Eulerian circuit.

Explanation: The study materials state that Dijkstra's algorithm starts at the source with distance 0. It also mentions choosing the *unvisited* node with the *smallest* distance, not the largest visited. It is for shortest path, not longest path, and it does not involve duplicating edges for Eulerian circuits, which is part of the Chinese Postman problem.