(NOTE: The question does not specify whether to maximize or minimize the allocations. So we assume it’s a minimization problem while solving)

Consider the matrix:

• Subtracting the smallest element in each row, from all the other row elements:

Number of lines = 3 < order of matrix = 5

• Subtracting the smallest element in each column, from all the other column elements:

Allocation can be made as shown. However, each row and column do not have one allocation. Drawing minimum number of lines through the zeroes:

• Subtracting the minimum uncovered element from all the other uncovered elements, and adding it to the elements where 2 lines intersect:

Allocation can be made as shown above. Each row and column still do not have one allocation. Drawing minimum number of lines through the zeroes:

• Subtracting the minimum uncovered element from all the other uncovered elements, and adding it to the elements where 2 lines intersect:

The remaining zeroes can be allocated in 2 possible ways (alternate solution):

Making the same allocations in the original matrix:

Minimum = 11 + 7 + 17 + 12 + 13 = 60

AND

Minimum = 11 + 10 + 17 + 6 + 16 = 60

Joy taxi has four taxi,1,2,3,4 & there are four coustmers,P,Q,R,S requring taxi. The distance between the taxi and the costomer are given in the table below, in kilometers. The Taxi company wish to assginthe taxis tocustomers so that the distance traveled is aminimum through Hungaian Model.

                P         Q        R      S
        1      10       8          4      6

Taxi 2 6 4 12 8 3 14 10 8 2 4 4 14 10 8