
I 
II 
III 
IV 
A 
8 
26 
17 
11 
B 
13 
28 
4 
26 
C 
38 
19 
18 
15 
D 
19 
26 
24 
10 
Step 1:Identity the minimum element in each row and subtract it from every element of that row

I 
II 
III 
Iv 
A 
0 
18 
9 
3 
B 
9 
24 
0 
22 
C 
23 
4 
3 
0 
D 
9 
16 
14 
0 
Step 2:Identity the minimum element in each column and subtract it from every element of that column

I 
II 
III 
Iv 
A 
0 
14 
9 
3 
B 
9 
20 
0 
22 
C 
23 
0 
3 
0 
D 
9 
12 
14 
0 
Step 3:Cover all 0's with a minimum number of lines

I 
II 
III 
Iv 
A 
0 
14 
9 
3 
B 
9 
20 
0 
22 
C 
23 
0 
3 
0 
D 
9 
12 
14 
0 
Step 4: (Optimal Assignment) There are 4 lines required.The 0's covers an optimal assignment.

I 
II 
III 
Iv 
A 
0 
14 
9 
3 
B 
9 
20 
0 
22 
C 
23 
0 
3 
0 
D 
9 
12 
14 
0 
This corresponds to the following optimal assignment in original cost matrix

I 
II 
III 
Iv 
A 
8 
26 
17 
11 
B 
13 
28 
4 
26 
C 
38 
19 
18 
15 
D 
39 
26 
24 
10 
The total cost of assignment=A(I) +B(III)+C(II)+D(Iv)=8+19+4+10=41
Hence,Option(B) A(I) B(III) C(II) D(Iv)is the correct choice here.
References:http://www.universalteacherpublications.com/univ/ebooks/or/Ch6/hungar.htm
http://www.math.harvard.edu/archive/20_spring_05/handouts/assignment_overheads.pdf
http://www.hungarianalgorithm.com/solve.php (Online Calculator)