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Maharashtra State BoardHSC Commerce (English Medium) 12th Standard Board Exam
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A Departmental Head Has Three Jobs and Four Subordinates. the Subordinates Differ in Their Capabilities and the Jobs Differ in Their Work Contents. - Mathematics and Statistics

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Question

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

Solution

As the problem is unbalanced a dummy · job IV is introduced with zero performance as, the for:

  I II III IV
A 7 3 5 0
B 2 7 4 0
C 6 5 3 0
D 3 4 7 0

As minimum element of each row is 'O' hence minimum element of each column is subtracted from all the elements of that column,

  I II III IV
A 5 0 2 0
B 0 4 1 0
C 4 2 0 0
D 1 1 4 0

All the zeros of the above matrix a re covered with minimum number of lines is as below :

As the number of lines covering zeros is equal to the number of rows and columns. hence the optional solution is obtained it is as shown below :

As D gets a dummy job N, hence the assignment is as shown below :

A → Job II
B → Job I
C → Job III
and performance is 3 + 2 + 3 = 8 units

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Assignment Problem
  Is there an error in this question or solution?
Q 5.B.iii
2013-2014 (October)

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2013-2014 (October) (with solutions)
Q 5.B.iii | 4 marks

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Hence, total (minimum) processing cost = 25 + 21 + 19 + 34 = ₹`square`


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