Section A
Q1.
(a)
A department head has four subordinates and four tasks to be performed. The subordinates differ in efficiency and the tasks differ in their intrinsic difficulty. His estimate of the time each man would take to perform each task is given in the matrix below : Men
Task
E
F
G
H
A
18
26
17
11
B
13
28
14
26
C
38
19
18
15
D
19
26
24
10
How should the tasks be allocated to a man so as to minimize the total man hours?
(b)
There are four villages V1, V2, V3 and V4 which are affected due to floods. Food items are to be dropped in these villages by aircrafts A1, A2 and A3. Details of trips are given in the following table : V1
V2
V3
V4
Total Number of Trips from Ai
A1
2
5
9
10
50
A2
10
8
6
3
60
A3
8
10
5
3
40
Total
Number of Trips from Vj
30
50
60
40
Solve the transportation problem to drop maximum food.
(c)
Solve the following zero-sum game for two persons. Obtain the optimum strategies for both players and value of the game. Player A
2
4
1
Player B
3
-1
2
-1
2
3
