Maharashtra State BoardHSC Commerce 12th Board Exam
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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 - Mathematics and Statistics

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Sum

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?

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Solution

We can express the matrix form

`[(31,25,33,29), (25,24,23,21), (19,21,23,24), (38,36,34,40)]`

Subtracting the smallest element in each row from every element of it,

`[(6,0,8,4), (4,3,2,0), (0,2,4,5), (4,2,0,6)]`

Subtracting the smallest element In each column from very element of it.

`[(6,0,8,4), (4,3,2,0), (0,2,4,5), (4,2,0,6)]`

All the zeros of the above matrix are covered with minimum number of lines as below :

No. of lines = No. of rows/columns

Assignment of jobs :

A → Q, B → S, C → P, D → R

Minimum cost = 25 + 21 + 19 + 34

                        = Rs 99

Concept: Assignment Problem
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