# 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

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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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