MCQ(s) On Optimization Research Unit 1: Applications of LP (2024)

Question: 1

What is the main objective of the transportation problem in linear programming?

1. To minimize the transportation time
2. To minimize the transportation cost
3. To maximize the number of routes
4. To maximize the transportation distance

Question: 2

In the transportation problem, what do the supply constraints represent?

1. The maximum demand at each destination
2. The minimum transportation cost
3. The availability of goods at each source
4. The capacity of each transportation route

Question: 3

Which method is commonly used to find the initial feasible solution of a transportation problem?

1. Hungarian method
2. Simplex method
3. Northwest corner method
4. Dijkstra's algorithm

Question: 4

In the context of the assignment problem, what does the objective function typically seek to optimize?

1. The total time
2. The total cost
3. The total distance
4. The total resources

Question: 5

What is the key difference between the transportation problem and the assignment problem?

1. The transportation problem deals with minimizing costs, while the assignment problem deals with maximizing profits
2. The transportation problem involves sources and destinations, while the assignment problem involves agents and tasks
3. The transportation problem is solved using the Hungarian method, while the assignment problem is solved using the Simplex method
4. The transportation problem is linear, while the assignment problem is nonlinear

Question: 6

Which of the following algorithms is commonly used to solve the assignment problem?

1. Prim's algorithm
2. Kruskal's algorithm
3. Hungarian algorithm
4. Floyd-Warshall algorithm

Question: 7

What is the term used for a solution in the transportation problem where all supply and demand constraints are satisfied?

1. Feasible solution
2. Optimal solution
3. Degenerate solution
4. Unbounded solution

Question: 8

In a balanced transportation problem, what is true about the total supply and total demand?

1. Total supply is less than total demand
2. Total supply is greater than total demand
3. Total supply equals total demand
4. Total supply and demand are unrelated

Question: 9

Which of the following represents an assignment problem scenario?

1. Distributing goods from warehouses to stores
2. Assigning workers to specific jobs
3. Allocating resources to multiple projects
4. Scheduling flights between cities

Question: 10

In the transportation problem, what does the term 'degeneracy' refer to?

1. A situation where the supply exceeds the demand
2. A situation where multiple optimal solutions exist
3. A situation where the number of allocations is less than \( m + n - 1 \)
4. A situation where there are infeasible solutions