Question

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?

Answer 1

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