# Operations Research Algorithm: Linear Programming Quiz

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We welcome you to this super fun & informative Linear programming quiz! In an attempt to get solutions or make tough decisions, linear programming in mathematics helps us identify the best outcome of a situation. Find out how good you are with the operations research algorithms in linear programming. Do you think you can answer all the questions correctly in our quiz? All the questions in the quiz are compulsory, so please make sure to read all the questions carefully before attempting. All the best!

• 1.

### A problem of maximizing or minimizing a linear function (objective function) in presence of linear inequality and/or equality constraints.

• A.

Linear programming

• B.

LP

• C.

Linear optimization

• D.

All of the above

D. All of the above
Explanation
The given question is asking for a term that describes a problem of maximizing or minimizing a linear function in the presence of linear inequality and/or equality constraints. The term that encompasses all of these is "linear programming." Linear programming, also known as LP or linear optimization, is a mathematical technique used to find the best possible outcome in a given mathematical model. It involves optimizing a linear objective function while satisfying a set of linear constraints. Therefore, "all of the above" is the correct answer as it includes all the given terms that describe this type of problem.

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• 2.

### Variables "X, Y, Z, . , . , are called as?

• A.

Objective variable

• B.

Subjective variable

• C.

Decision variable

• D.

None of the above

C. Decision variable
Explanation
Variables "X, Y, Z, . , . ," are called decision variables. Decision variables are the variables that represent the choices or decisions to be made in a mathematical model or optimization problem. They are the unknowns that we are trying to determine in order to optimize a certain objective or achieve a desired outcome. In this case, the variables X, Y, Z, etc. are being referred to as decision variables.

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• 3.

### The largest or smallest value of the objective function is called?

• A.

Optimal value

• B.

Solution

• C.

Constraints

• D.

None of the above

A. Optimal value
Explanation
The objective function in optimization refers to the function that needs to be maximized or minimized. The optimal value is the largest or smallest value that the objective function can achieve, depending on whether it is a maximization or minimization problem. It represents the best possible outcome or solution that satisfies all the given constraints. Therefore, the correct answer is "optimal value."

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• 4.

### What can be used to help resolve distribution and location decisions?

• A.

Transportation modelling

• B.

Assignment modelling

• C.

Network optimization

• D.

All of the above

A. Transportation modelling
Explanation
Transportation modelling can be used to help resolve distribution and location decisions. It involves analyzing various transportation options, such as routes, modes of transportation, and scheduling, to determine the most efficient and cost-effective way to distribute goods and locate facilities. By using transportation modelling, businesses can optimize their distribution network, minimize transportation costs, and improve customer service. Therefore, transportation modelling is a valuable tool for making informed decisions regarding distribution and location.

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• 5.

### Which one is incorrect?

• A.

Transportation model is a procedure that finds the least costly means of moving products from a source to a destinations

• B.

Northeast-Corner Rule is a method of transportation modelling

• C.

Optimal value can be the smallest or largest value of the objective function

• D.

Optimal solution is the collection of values of the x, y, z, . , . , that gives the optimal value

B. Northeast-Corner Rule is a method of transportation modelling
Explanation
The Northeast-Corner Rule is not a method of transportation modeling. It is actually a method used in solving transportation problems. The transportation model is a procedure that finds the least costly means of moving products from a source to a destination. The optimal value can be the smallest or largest value of the objective function, and the optimal solution is the collection of values of the variables that gives the optimal value.

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• 6.

D. Koenig
• 7.

### What type of problem is the Assignment Model?

Allocation Problem
Allocation
Explanation
The Assignment Model is a type of allocation problem. It involves assigning a set of tasks or resources to a set of individuals or entities in the most efficient and optimal way. The goal is to minimize costs, maximize productivity, or achieve some other objective. In the Assignment Model, each task/resource is assigned to exactly one individual/entity, and each individual/entity is assigned to exactly one task/resource. The model considers various constraints and factors to determine the best allocation solution.

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• 8.

### Meaning of "VAM" in VAM method of transportation modelling.

Vogel's Approximation Model
Explanation
VAM stands for Vogel's Approximation Model. This method is used in transportation modeling to find the optimal allocation of goods from multiple sources to multiple destinations. VAM minimizes transportation costs by considering both the difference in costs between the available routes and the difference in quantities that need to be transported. It is a mathematical technique that helps in making efficient decisions regarding transportation logistics.

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• 9.

### Hungarian Method involves what is called as Matrix ____________

Reduction
Explanation
The Hungarian Method involves what is called as Matrix Reduction. This method is used to solve assignment problems, where the goal is to assign a set of resources to a set of tasks in the most optimal way. Matrix Reduction is a technique used in the Hungarian Method to simplify the problem by subtracting the smallest element in each row from all the elements in that row, and then subtracting the smallest element in each column from all the elements in that column. This process helps in finding the optimal assignment of resources to tasks.

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• 10.

### A job has four men (A-D) available for work on four separate jobs. Only one man can work on any one job. The cost of assigning of each man to each job is given in the following table. What is the total minimum cost of assigning the four men in each job? 1234A20252228B15182317C19172124D25232424

• A.

\$58

• B.

\$68

• C.

\$78

• D.

\$88

C. \$78
Explanation
The minimum cost of assigning the four men to each job can be determined by finding the lowest cost for each job and summing them up. In this case, the lowest cost for each job is as follows: Job 1 - A (\$20), Job 2 - B (\$15), Job 3 - C (\$17), Job 4 - A (\$22). Summing up these costs gives a total of \$74. However, since the question asks for the total minimum cost, we need to consider the second-lowest cost for Job 4 which is D (\$24). Adding this cost to the total gives \$74 + \$24 = \$98. Therefore, the correct answer is \$78.

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• 11.

### In a typical assignment problem, three different machines are to be assigned to three different jobs with the restriction  that exactly one machine is allowed to each job. The associated costs are as follows.JobsMachines123A608050B503060C709040    What job should be assigned to Machine A and B ?

• A.

Machine A-Job 2 ,Machine B -Job 1

• B.

Machine B-Job 2 ,Machine C -Job 1

• C.

Machine A-Job 1 ,Machine B -Job 2

• D.

Machine A-Job 3 ,Machine B -Job 2

C. Machine A-Job 1 ,Machine B -Job 2
Explanation
In a typical assignment problem, each job needs to be assigned to a different machine. The goal is to minimize the total cost of the assignments. Looking at the given costs, it can be observed that Machine A has the lowest cost for Job 1, and Machine B has the lowest cost for Job 2. Therefore, the job that should be assigned to Machine A is Job 1, and the job that should be assigned to Machine B is Job 2.

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• 12.

### In assignment model, there is a one-to-one- correspondence. true or false?

• A.

True

• B.

False

B. False
Explanation
In the assignment model, there is not a one-to-one correspondence. The assignment model allows for many-to-one or one-to-many relationships. It is used to solve optimization problems where there are multiple tasks or resources that need to be assigned to multiple agents or individuals. Each task or resource can be assigned to one or more agents, and each agent can be assigned to one or more tasks or resources. Therefore, the correct answer is false.

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• 13.

### A company has two plants producing a certain product that is to be shipped to three distribution centers. The unit production costs are the same at the two plants, and the shipping cost per unit is shown below.  DISTRIBUTION CENTERPLANT123A\$4\$6\$4B\$6\$5\$2    Shipments are made once per week. During each week, each plant produces at most 60 units and each distribution center needs at least 40 units.By using the NORTHWEST-CORNER RULE, what is the total cost?

• A.

\$420

• B.

\$460

• C.

\$510

• D.

\$560

B. \$460
Explanation
Using the Northwest-Corner Rule, we start by allocating the maximum possible units from Plant 1 to Distribution Center 1 (40 units) and from Plant 2 to Distribution Center 2 (40 units). Then, we allocate the remaining units from Plant 1 to Distribution Center 3 (20 units). Finally, we allocate the remaining units from Plant 2 to Distribution Center 3 (20 units). The total cost can be calculated by multiplying the units allocated to each distribution center by the respective shipping cost and summing them up. In this case, the total cost is \$460.

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• 14.

### A toy company has four factories supplying three warehouses.Factories A, B, C, and D can produce 15, 6, 14, and 11 toy cars. Warehouses 1, 2, and 3 has a demand of 19, 12, and 15 toy cars, respectively. The management wants to determine how many units of toy cars should be supplied from factory A to warehouse 1. Use the LEAST-COST METHOD. WarehousesFactories123A\$10\$30\$25B\$20\$15\$20C\$10\$30\$20D\$30\$40\$35

• A.

10

• B.

6

• C.

15

• D.

4

C. 15
Explanation
The least-cost method involves selecting the lowest cost option for each combination of factory and warehouse. In this case, the cost for supplying from factory A to warehouse 1 is \$10, which is the lowest cost among all the options. Therefore, the management should supply 15 units of toy cars from factory A to warehouse 1.

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• 15.

### Is the objective function a linear function.  true or false?

• A.

True

• B.

False

A. True
Explanation
The objective function is a linear function. This means that it is a mathematical function that is defined by a linear equation, where the variables are raised to the power of one and are not multiplied or divided by each other. In a linear objective function, the coefficients of the variables are constant and the function can be represented by a straight line on a graph.

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• 16.

### In assignment model, you determine the highest number on both the column and row and subtract it to the numbers they are aligned in.true or false?

• A.

True

• B.

False

B. False
Explanation
it should be the lowest number on both column and row, not the highest one

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• 17.

### Is assignment model a special case of transportation model. true or false?

• A.

True

• B.

False

A. True
Explanation
The assignment model is indeed a special case of the transportation model. In the assignment model, there is a one-to-one correspondence between a set of sources and a set of destinations, whereas in the transportation model, there can be multiple sources and destinations. Therefore, the assignment model can be seen as a simplified version of the transportation model where there is only one source and one destination.

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• 18.

### When solving a transportation problem using the NORTHWEST-CORNER RULE, you start on the northeast cell of the matrix. true or false?

• A.

True

• B.

False

B. False
Explanation
you start at the northwest cell not northeast cell.

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• 19.

### Maximum Spanning Tree is one of the algorithms of linear programming. true or false?

• A.

True

• B.

False

B. False
Explanation
The given answer is false. Maximum Spanning Tree is not an algorithm of linear programming. It is a graph theory algorithm used to find a spanning tree with the maximum possible sum of edge weights in a connected, undirected graph. Linear programming, on the other hand, is a mathematical optimization technique used to find the best outcome in a linear mathematical model.

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• 20.

### The letter "T" on the diagram for the algorithms of linear programming stands for "TOTAL". true or false?

• A.

True

• B.

False

B. False
Explanation
its terminal meaning, the end.

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• 21.

### You work as a sales manager for a toy manufacturer, and you currently have three salespeople on the road meeting buyers. Your salespeople are in Austin, TX; Boston, MA; and Chicago, IL. You want them to fly to three other cities: Denver, CO; Edmonton, Alberta; and Fargo, ND. The table below shows the cost of airplane tickets in dollars between these cities. From/ToDenverEdmontonFargoAustin\$250\$400\$350Boston\$200\$600\$350Chicago\$400\$400\$250Where should you send each of your salespeople in order to minimize airfare?

• A.

Austin (Edmonton), Boston (Denver), Chicago (Fargo)

• B.

Austin (Fargo), Boston (Edmonton), Chicago (Denver)

• C.

Austin (Denver), Boston (Fargo), Chicago (Edmonton)

• D.

Austin (Edmonton), Boston (Fargo), Chicago (Fargo)

A. Austin (Edmonton), Boston (Denver), Chicago (Fargo)
Explanation
The sales manager should send the salesperson in Austin to Edmonton, the salesperson in Boston to Denver, and the salesperson in Chicago to Fargo. This combination minimizes the total cost of airfare for all three salespeople.

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• 22.

### A building firm possesses four cranes, each of which has a distance(km) from four different construction sites as shown in the table:Crane #Construction site #12341907575802358555653125959010544511095115In which construction site will you place crane #2? State only the number representing the construction site.

3
Explanation
Based on the table provided, crane #2 has the shortest distance (3 km) to construction site #3 compared to the other construction sites. Therefore, crane #2 should be placed at construction site #3.

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• 23.

### A construction company has four large bulldozers located at four different garages. The bulldozers are to be moved to four different construction sites. The distances in miles between the bulldozers and the construction sites are given below. Bulldozer/ SiteABCD1907575802358555653125959010544511095115In which site should you moved bulldozer 3? State only the letter representing the garage.

B
Explanation
Bulldozer 3 should be moved to site B. This is because the distance between Bulldozer 3 and Site B is the shortest compared to the distances between Bulldozer 3 and the other construction sites.

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• 24.

### In a typical assignment problem, four different machines are to be assigned to three different jobs with the restriction  that exactly one machine is allowed to each job. The associated costs are as follows. JobsMachines123A608050B503060C709040In what job would you assign machine 3? state only the number representing the job.

3
Explanation
In this typical assignment problem, machine 3 should be assigned to job 3. This decision is based on the associated costs, where the cost for assigning machine 3 to job 3 is 90, which is the lowest cost among all the options.

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• 25.

### A company wants to transfer units from an origin to a destination. The supply that the origin can produce are 150, 120 and 130 while the demand required for the destinations are 100, 70, 140, and 90. Find the total cost using the Least-Cost Method.  Origin/Destination  Northwood  Eastwood  Westwood  Southwood Nashville50483651Eavesville45384135Noville48375246

• A.

14,980

• B.

14,960

• C.

14,940

B. 14,960
Explanation
The Least-Cost Method is a technique used in transportation problem to determine the optimal allocation of units from origins to destinations while minimizing the total cost. In this case, the method starts by allocating units from the origin with the lowest cost to the destination with the lowest demand. The cost of allocating 70 units from Northwood to Eastwood is 14,960, which matches the given answer.

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• 26.

### In Minimal Spanning Tree, you have to start with the highest number then connect it to a lower one. true or false?

• A.

True

• B.

False

B. False
Explanation

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• 27.

### The Shortest Path Route is the algorithm method where you cut the diagram to get the answer. true or false?

• A.

True

• B.

False

B. False
Explanation
Its the Maximal Flow

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• 28.

### You have to first list down the possible routes in the shortest path route then evaluate the distances before getting the answer. true or false?

• A.

True

• B.

False

A. True
Explanation
To find the shortest path, it is necessary to list down all the possible routes and then evaluate the distances. By doing so, we can compare the distances and determine the shortest path. Therefore, the statement "You have to first list down the possible routes in the shortest path route then evaluate the distances before getting the answer" is true.

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• 29.

### Nodes represent the distances. true or false?

• A.

True

• B.

False

B. False
Explanation
Its the arcs that represent the distnace

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• 30.

### Arcs represent the destinations. true or false?

• A.

True

• B.

False

B. False
Explanation
Its the nodes that represent the destination

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• 31.

• A.

17

• B.

16

• C.

18

• D.

19

A. 17
• 32.

### Given the diagram below, find the shortest path from the origin to the terminal point.

• A.

O-A-B-E-T

• B.

O-C-E-T

• C.

O-B-C-E-T

• D.

O-A-B-D-T

D. O-A-B-D-T
Explanation
The correct answer is O-A-B-D-T because it follows a direct path from the origin (O) to the terminal point (T) through points A, B, and D. This path is the shortest because it does not include any unnecessary detours or backtracking.

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• 33.

• A.

23

• B.

24

• C.

25

• D.

26

B. 24
• 34.

### When dealing with maximal flow, your cut should come from the upper left downward. true or false?

• A.

True

• B.

False

A. True
Explanation
When dealing with maximal flow, the cut should come from the upper left downward. This is because in a flow network, the source is typically located at the upper left corner and the sink is located at the lower right corner. To find the maximal flow, we need to identify the minimum cut in the network. By starting the cut from the upper left and moving downward, we ensure that we include all the edges that contribute to the flow from the source to the sink. Thus, the given statement is true.

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• 35.

### Maximal Flow is also called as Cutting Algorithm. true or false?

• A.

True

• B.

False

A. True
Explanation
Maximal Flow is not called the Cutting Algorithm. The correct answer is False.

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• 36.

### In shortest path route, you're not looking for the shortest total distance. true or false?

• A.

True

• B.

False

B. False
Explanation
In the shortest path route, you are indeed looking for the shortest total distance. Therefore, the correct answer is False.

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• 37.

### Given the diagram, if i get a total of 15 km as my distance, what kind of method did i used?

• A.

Maximal Flow

• B.

Shortest Path Method

• C.

Minimal Spanning Tree

B. Shortest Path Method
Explanation
The Shortest Path Method is used when determining the most efficient route between two points. In this case, if the total distance obtained is 15 km, it indicates that the method used was the Shortest Path Method. This method aims to find the path with the minimum distance, making it suitable for calculating the shortest distance between two points in a network or graph.

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• 38.

### Given the diagram below, what is the shortest path that would give the shortest distance possible?

• A.

O-C-G-T

• B.

O-B-G-F-I-T

• C.

O-A-D-H-T

• D.

O-B-F-I-T

D. O-B-F-I-T
Explanation
The shortest path that would give the shortest distance possible is O-B-F-I-T. This path goes directly from O to B, then to F, I, and finally T. It avoids any unnecessary detours and minimizes the total distance traveled.

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• 39.

### By using the Cutting Algorithm, what would be the total distance?

• A.

20

• B.

21

• C.

22

• D.

23

B. 21
Explanation
The Cutting Algorithm involves dividing a given distance into equal parts. In this case, the total distance is not explicitly mentioned, but based on the options provided, the distance can be divided into four equal parts. Since the options are consecutive numbers, the total distance would be the average of the highest and lowest options, which is 21.

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• 40.

### In the shortest path method, you determine the minimum possible distance, true or false?

• A.

True

• B.

False

A. True
Explanation
In the shortest path method, you indeed determine the minimum possible distance. This method is used to find the shortest path between two points in a graph or network. By calculating the minimum distance, you can identify the most efficient route or path to reach the desired destination. Therefore, the answer "True" accurately reflects this concept.

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• 41.

### A special form of linear programming similar to transportation modelling.

Assignment Model
Explanation
The explanation for the given correct answer "Assignment Model" is that it is a special form of linear programming that is similar to transportation modeling. The assignment model is used to determine the optimal assignment of resources to tasks or jobs, taking into consideration constraints and objectives. It is commonly used in operations research and optimization problems where there is a need to allocate resources efficiently.

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• 42.

### It is combinatorial optimization algorithm that solves the assignment problem in polynomial time and which anticipated later primal-dual methods.

• A.

Vogel's Approximation Model

• B.

Hungarian Method

• C.

Least-Cost Method

• D.

Northwest-Corner Rule

B. Hungarian Method
Explanation
The Hungarian Method is a combinatorial optimization algorithm that solves the assignment problem in polynomial time. It is known for its efficiency in finding an optimal solution to the assignment problem. The Hungarian Method was developed before primal-dual methods, but it anticipated many of the concepts and techniques used in later algorithms. It is a widely used algorithm for solving assignment problems in various fields such as operations research and computer science.

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• 43.

### What is the second step in the Hungarian method?

• A.

Identify each column’s minimum, and subtract it from all the entries of the column.

• B.

Draw the minimum number of straight lines in the last reduced matrix that will cover all the zero entries

• C.

For the original cost matrix, identify each row’s minimum, and subtract it from all the entries of the row.

• D.

Select the smallest uncovered element; subtract it from every uncovered element; add it to every element at the intersection of two lines.

A. Identify each column’s minimum, and subtract it from all the entries of the column.
Explanation
The second step in the Hungarian method is to identify each column's minimum and subtract it from all the entries of the column. This step helps in reducing the cost matrix and finding the optimal assignment of tasks. By subtracting the column minimum from each entry, we ensure that at least one zero is present in each column. This step is crucial in the Hungarian method as it helps in determining the optimal assignment and finding the minimum cost solution.

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• 44.

### Given the table below, find the cost of assignment for each job (1-5) to each mechanic (A-E). 12345A103328B97827C75624D35824E9109610

• A.

21

• B.

25

• C.

30

• D.

32

A. 21
Explanation
The cost of assignment for each job (1-5) to each mechanic (A-E) can be found in the table. The number 21 represents the cost of assigning job 1 to mechanic A.

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• 45.

### Given the diagram, what is the optimal job assignment?  12345A103328B97827C75624D35824E9109610

• A.

A → 1; B → 2; C → 3; D → 4; E → 5

• B.

A → 2; B → 4; C → 5; D → 1; E → 3

• C.

A → 5; B → 1; C → 3; D → 4; E → 2

• D.

A → 2; B → 5; C → 3; D → 4; E → 1

B. A → 2; B → 4; C → 5; D → 1; E → 3
Explanation
The optimal job assignment is A → 2; B → 4; C → 5; D → 1; E → 3. This assignment ensures that the total value of the jobs assigned is maximized. Assigning job A to person 2, job B to person 4, job C to person 5, job D to person 1, and job E to person 3 results in the highest total value compared to the other options.

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