English

In an assignment problem, if number of column is greater than number of rows, then a dummy column is added.

Question

Options

True
False

MCQ

True or False

Solution

This statement is False.

Explanation:

In an assignment problem, if the number of rows is less than columns, a dummy row is added to make it a square matrix.
A dummy column is added only when rows exceed columns, not the other way around.

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Assignment Problem

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Q 3.08 Q 3.07 Q 3.09

Chapter 7: Assignment Problem and Sequencing - Miscellaneous Exercise 7 [Page 128]

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Balbharati Mathematics and Statistics 2 (Commerce) [English] Standard 12 Maharashtra State Board

Chapter 7 Assignment Problem and Sequencing
Miscellaneous Exercise 7 | Q 3.08 | Page 128

2022-2023 (March) Official (with solutions)

Q 4.B.iii | 1 mark

2023-2024 (July) Official (with solutions)

Q 4.B.iii | 1 mark

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RELATED QUESTIONS

A job production unit has four jobs A, B, C, D which can be manufactured on each of the four machines P, Q, R and S. The processing cost of each job is given in the following table:

Jobs	Machines
	P	Q	R	S
	Processing Cost (Rs.)
A	31	25	33	29
B	25	24	23	21
C	19	21	23	24
D	38	36	34	40

How should the jobs be assigned to the four machines so that the total processing cost is minimum?

Solve the following minimal assignment problem and hence find the minimum value :

	I	II	III	IV
A	2	10	9	7
B	13	2	12	2
C	3	4	6	1
D	4	15	4	9

Solve the following minimal assignment problem :

Machines	A	B	C	D	E
M₁	27	18	∞	20	21
M₂	31	24	21	12	17
M₃	20	17	20	∞	16
M₄	21	28	20	16	27

A departmental head has three jobs and four subordinates. The subordinates differ in their capabilities and the jobs differ in their work
contents. With the help of the performance matrix given below, find out which of the four subordinates should be assigned which jobs ?

Subordinates	Jobs
Subordinates	I	II	III
A	7	3	5
B	2	7	4
C	6	5	3
D	3	4	7

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The assignment problem is said to be balanced if ______.

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In assignment problem, each facility is capable of performing each task.

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It is not necessary to express an assignment problem into n x n matrix.

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	I	II	III	IV	V
A	150	120	175	180	200
B	125	110	120	150	165
C	130	100	145	160	175
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?

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The assignment problem is said to be balanced if ______

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

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

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Give mathematical form of Assignment problem

What is the difference between Assignment Problem and Transportation Problem?

Three jobs A, B and C one to be assigned to three machines U, V and W. The processing cost for each job machine combination is shown in the matrix given below. Determine the allocation that minimizes the overall processing cost.

		Machine
		U	V	W
Jobs	A	17	25	31
	B	10	25	16
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(cost is in ₹ per unit)

A computer centre has got three expert programmers. The centre needs three application programmes to be developed. The head of the computer centre, after studying carefully the programmes to be developed, estimates the computer time in minitues required by the experts to the application programme as follows.

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Programmers	1	120	100	80
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A departmental head has four subordinates and four tasks to be performed. The subordinates differ in efficiency and the tasks differ in their intrinsic difficulty. His estimates of the time each man would take to perform each task is given below:

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Subordinates	P	8	26	17	11
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	R	38	19	18	15
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C	4	9	6	9
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		To
		7	8	9	10	11	12
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	2	12	19	39	55	71	40
	3	17	29	50	41	22	22
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A	3	11	10	8
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