# SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 chapter 3 - Assignment Problem and Sequencing [Latest edition]

## Chapter 3: Assignment Problem and Sequencing

Q.1Q.2Q.3Q.4Q.5
Q.1

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 Chapter 3 Assignment Problem and Sequencing Q.1

#### MCQ [1 Mark]

Q.1 | Q 1

Choose the correct alternative:

The assignment problem is generally defined as a problem of ______

• maximization

• minimization

• allocation

• restriction

Q.1 | Q 2

Choose the correct alternative:

Assignment Problem is special case of ______

• Linear Programming Problem

• Unbalanced Problem

• Restricted Problem

• Sequencing Problem

Q.1 | Q 3

Choose the correct alternative:

The assignment problem is solved by ______

• Simplex method

• Hungarian method

• Vector method

• Graphical method

Q.1 | Q 4

Choose the correct alternative:

The cost matrix of an unbalanced assignment problem is not a ______

• unit matrix

• triangular matrix

• rectangular matrix

• square matrix

Q.1 | Q 5

Choose the correct alternative:

When an assignment problem has more than one solution, then it is ______

• double optimal solution

• infinite optimal solution

• multiple optimal solution

• dual optimal solution

Q.1 | Q 6

Choose the correct alternative:

The assignment problem is said to be balanced if ______

• no. of rows = no. of columns

• no. of rows ≠ no. of columns

• no. of rows < no. of columns

• no. of rows > no. of columns

Q.1 | Q 7

Choose the correct alternative:

 Machine Job A B C D I 5 6 8 4 II 4 7 9 10

The optimal sequence for above data is

• CDBA

• DBCA

• BCDA

• ABCD

Q.1 | Q 8

Choose the correct alternative:

In sequencing, an optimal path that minimizes ______

• Elapsed time

• Idle time

• Both elapsed time and idle time

Q.1 | Q 9

Choose the correct alternative:

If there are 3 machines A, B and C, conditions for reducing a 3 machine problem to a 2 machine problem with respect to minimum processing time is ______

• Min Ai ≥ Max Bi OR Min Ci ≥ Max Bi, i = 1, 2, 3…n

• Min Ai ≤ Max Bi OR Min C ≤ Max Bi, i = 1, 2, 3…n

• Max Ai ≥ Min Bi OR Max B ≥ Min Ai, i = 1, 2, 3…n

• Max Ai ≤ Min Bi OR Max B ≤ Min Ai, i = 1, 2, 3…n

Q.1 | Q 10

Choose the correct alternative:

The objective of sequencing problem is ______

• to find the order in which jobs are to be made

• to find the time required for the completing all the job on hand

• to find the sequence in which jobs on hand are to be processed to minimize the total time required for processing the jobs

• to maximization the cost

Q.1 | Q 11

Choose the correct alternative:

If there are n jobs and m machines, then there will be _______ sequence of doing jobs.

• mn

• m(n!)

• nm

• (n!)m

Q.1 | Q 12

Choose the correct alternative:

In solving 2 machine and n jobs sequencing problem, the following assumption is wrong

• No passing is allowed

• Processing times are known

• Handling time is negligible

• The time of passing depends on the order of machining

Q.2

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 Chapter 3 Assignment Problem and Sequencing Q.2

#### Fill in the blanks [1 Mark]

Q.2 | Q 1

If the given matrix is ______ matrix, the assignment problem is called balanced problem

Q.2 | Q 2

An unbalanced assignment problems can be balanced by adding dummy rows or columns with ______ cost

Q.2 | Q 3

A ______ assignment problem does not allow some worker(s) to be assign to some job(s)

Q.2 | Q 4

In an assignment problem if number of rows is greater than number of columns, then dummy ______ is added

Q.2 | Q 5

The Hungarian method is an ______ algorithm that solves an assignment problem

Q.2 | Q 6

In assignment problem each worker or machine is ______ capable of handling any job

Q.2 | Q 7

In sequencing problems one has to ______ the total processing time or cost

Q.2 | Q 8

In sequencing problem the time which required to complete all the jobs i.e. entire task is called ______

Q.2 | Q 9

______ time is the time when the machine is available but is waiting for a job to be processed

Q.2 | Q 10

In sequencing problem the time required to transfer a job from one machine to another is ______

Q.2 | Q 11
 Book A B C D Printing 5 8 10 7 Data Entry 7 4 3 6

The optimum sequence for the above data is ______

Q.2 | Q 12

In sequencing problem one has to determine the ______ in which jobs has to processed through the machines

Q.3

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 Chapter 3 Assignment Problem and Sequencing Q.3

#### [1 Mark]

Q.3 | Q 1

State whether the following statement is True or False:

The objective of an assignment problem is to assign number of jobs to equal number of persons at maximum cost

• True

• False

Q.3 | Q 2

State whether the following statement is True or False:

To convert the assignment problem into maximization problem, the smallest element in the matrix is to deducted from all other elements

• True

• False

Q.3 | Q 3

State whether the following statement is True or False:

Optimal assignments are made in the Hungarian method to cells in the reduced matrix that contain a zero

• True

• False

Q.3 | Q 4

State whether the following statement is True or False:

In assignment problem, if number of columns is greater than number of rows, then a dummy row is added

• True

• False

Q.3 | Q 5

State whether the following statement is True or False:

The Hungarian method is used to assign n jobs on 2 machines to get the optimal sequence

• True

• False

Q.3 | Q 6

State whether the following statement is True or False:

In assignment problem each worker or machine is assigned only one job

• True

• False

Q.3 | Q 7

State whether the following statement is True or False:

One of the assumptions is made while sequencing n jobs on 2 machines is: two jobs must be loaded at a time on any machine

• True

• False

Q.3 | Q 8

State whether the following statement is True or False:

The Total Elapsed is the time required to complete all the jobs i.e. entire task

• True

• False

Q.3 | Q 9

State whether the following statement is True or False:

The idle time for a machine is the when machine is available but is not waiting for any job to be processed

• True

• False

Q.3 | Q 10

State whether the following statement is True or False:

In sequencing problem the processing times are dependent of order of processing the jobs on machine

• True

• False

Q.3 | Q 11

State whether the following statement is True or False:

In sequencing problem each job once started on any machine must be processed still its completion

• True

• False

Q.3 | Q 12

State whether the following statement is True or False:

In sequencing problem each machine is of different type

• True

• False

Q.4

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 Chapter 3 Assignment Problem and Sequencing Q.4

#### Attempt the following questions [3 or 4 Marks]

Q.4 | Q 1

Four new machines M1, M2, M3 and M4 are to be installed in a machine shop. There are five vacant places A, B, C, D and E available. Because of limited space, machine M2 cannot be placed at C and M3 cannot be placed at A. The cost matrix is given below.

 Machines Places A B C D E M1 4 6 10 5 6 M2 7 4 – 5 4 M3 – 6 9 6 2 M4 9 3 7 2 3

Find the optimal assignment schedule

Q.4 | Q 2

Solve the following problem :

Solve the following assignment problem to maximize sales:

 Salesman Territories I II III IV V A 11 16 18 15 15 B 7 19 11 13 17 C 9 6 14 14 7 D 13 12 17 11 13
Q.4 | Q 3

Solve the following problem :

Consider the problem of assigning five operators to five machines. The assignment costs are given in following table.

 Operator Machine 1 2 3 4 5 A 6 6 – 3 7 B 8 5 3 4 5 C 10 4 6 – 4 D 8 3 7 8 3 E 7 6 8 10 2

Operator A cannot be assigned to machine 3 and operator C cannot be assigned to machine 4. Find the optimal assignment schedule.

Q.4 | Q 4

Find the assignments of salesman to various district which will yield maximum profit

 Salesman District 1 2 3 4 A 16 10 12 11 B 12 13 15 15 C 15 15 11 14 D 13 14 14 15
Q.4 | Q 5

A dairy plant has five milk tankers, I, II, III, IV and V. Three milk tankers are to be used on five delivery routes A, B, C, D and E. The distances (in kms) between the dairy plant and the delivery routes are given in the following distance matrix.

 I II III IV V A 150 120 175 180 200 B 125 110 120 150 165 C 130 100 145 160 170 D 40 40 70 70 100 E 45 25 60 70 95

How should the milk tankers be assigned to the chilling center so as to minimize the distance travelled?

Q.4 | Q 6

Solve the following problem :

Find the sequence that minimizes the total elapsed time to complete the following jobs. Each job is processed in order AB.

 Machines Jobs (Processing times in minutes) I II III IV V VI VII Machine A 12 6 5 11 5 7 6 Machine B 7 8 9 4 7 8 3

Determine the sequence for the jobs so as to minimize the processing time. Find the total elapsed time and the idle times for both the machines.

Q.4 | Q 7

Find the optimal sequence that minimizes total time required to complete the following jobs in the order ABC. The processing times are given in hours.

 Jobs I II III IV V VI VII Machine A 6 7 5 11 6 7 12 Machine B 4 3 2 5 1 5 3 Machine C 3 8 7 4 9 8 7
Q.4 | Q 8

Solve the following problem :

Five jobs must pass through a lathe and a surface grinder, in that order. The processing times in hours are shown below. Determine the optimal sequence of the jobs. Also find the idle time of each machine.

 Job I II III IV V Lathe 4 1 5 2 5 Surface grinder 3 2 4 3 6
Q.4 | Q 9

Solve the following problem :

A toy manufacturing company produces five types of toys. Each toy has to go through three machines A, B, C in the order ABC. The time required in hours for each process is given in the following table.

 Type 1 2 3 4 5 Machine A 16 20 12 14 22 Machine B 10 12 4 6 8 Machine C 8 18 16 12 10

Solve the problem for minimizing the total elapsed time.

Q.4 | Q 10

Find the sequence that minimizes total elapsed time to complete the following jobs in the order XY. Find the total elasped time and idle times for each machine.

 Jobs A B C D E Machine X 10 2 18 6 20 Machine Y 4 12 14 16 8
Q.5

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 Chapter 3 Assignment Problem and Sequencing Q.5

#### Activities [4 marks]

Q.5 | Q 1

For the following assignment problem minimize total man hours:

 Subordinates Required hours for task I II III IV A 7 25 26 10 B 12 27 3 25 C 37 18 17 14 D 18 25 23 9

Subtract the square element of each square from every element of that square

 Subordinates Required hours for task I II III IV A 0 18 19 3 B 9 24 0 22 C 23 4 3 0 D 9 16 14 0

Subtract the smallest element in each column from square of that column.

 Subordinates Required hours for task I II III IV A square square 19 square B square square 0 square C square square 3 square D square square 14 square

The lines covering all zeros is square to the order of matrix square

The assignment is made as follows:

 Subordinates Required hours for task I II III IV A 0 14 19 3 B 9 20 0 22 C 23 0 3 0 D 9 12 14 0

Optimum solution is shown as follows:

A → square, square → III, C → square, square → IV

Minimum hours required is square hours

Q.5 | Q 2

Solve the following problem of sequencing for minimizing the total elapsed time and idle time for both the machines.

 Job P Q R S T U M1 1 4 6 3 5 2 M2 3 6 8 8 1 5

The optimal sequence of the jobs as follows:

Total elasped time is obtained as follows:

 Job sequence Machine A Machine B Idle time forMachine B Time In Time Out Time In Time Out P square 1 1 square square U square 3 4 square square S square 6 9 square square Q square 10 17 square square R square 16 23 square square T square 21 31 square square

Total elapsed time T = square minutes

Idle time for Machine A = T – square = square minutes

Idle time for Machine B = square

Q.1Q.2Q.3Q.4Q.5

## SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 chapter 3 - Assignment Problem and Sequencing

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 chapter 3 (Assignment Problem and Sequencing) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the Maharashtra State Board 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 chapter 3 Assignment Problem and Sequencing are Assignment Problem, Hungarian Method of Solving Assignment Problem, Special Cases of Assignment Problem, Sequencing Problem, Types of Sequencing Problem, Finding an Optimal Sequence.

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