(Maximization)
Â
1.        A manufacturer has 5 machines and 5 workers working. The output for worker machine combination is given.
Workers |
Machines |
||||
1 |
2 |
3 |
4 |
5 |
|
W1 |
20 |
23 |
27 |
32 |
36 |
W2 |
19 |
23 |
29 |
34 |
40 |
W3 |
23 |
28 |
35 |
39 |
34 |
W4 |
21 |
24 |
31 |
37 |
42 |
W5 |
22 |
28 |
31 |
36 |
41 |
(i)Â Â Â Â Â Â Find worker machine combination that maximizes total output
(ii)Â Â Â Â Â If profit per unit is Rs. 10/-. Find total profit.
(Ans :  W1 ® 1, W2 ® 5, W3 ® 3, W4 ® 4, W5 ® 2; Total Output = 160 units, Total profit = Rs. 1600)
Â
2.        Four machines can do 4 jobs. The output per machine in units is given below. Determine the job machine combination for maximum profit.
Machine |
Jobs |
|||
1 |
2 |
3 |
4 |
|
M1 |
60 |
40 |
60 |
70 |
M2 |
20 |
60 |
50 |
70 |
M3 |
20 |
30 |
40 |
60 |
M4 |
30 |
10 |
30 |
40 |
(Ans :  M1 ® 1, M2 ® 2, M3 ® 4, M4 ® 3 OR M1 ® 3, M2 ® 2, M3 ® 4, M4 ® 1)
Â
3.        5 salesman are to be assigned 5 cities based on past performance data and following table sowing annual sales (in Rs. Lakhs). Find optimum assignment
 |
City |
||||
Salesman |
A |
B |
C |
D |
E |
S1 |
26 |
14 |
10 |
12 |
9 |
S2 |
31 |
27 |
30 |
14 |
16 |
S3 |
15 |
18 |
16 |
25 |
30 |
S4 |
17 |
12 |
21 |
30 |
25 |
S5 |
20 |
19 |
25 |
16 |
10 |
 (Ans :  S1 ® A, S2 ® B, S3 ® E, S4 ® D, S5 ® C; Sales = 26 + 27 + 30 + 30 + 25 = 138 lakhs)
4.        A five star hotel which has 4 banquet halls was used for functions. The halls are of same but with varying facilities. 4 parties approached to a hall for the function on same day. These parties were told that the first choice would cost Rs. 10,000 for the day. They were told to indicate the 2nd, 3rd & 4th preferences and the price they were willing to pay the two parties A & D told that they were not interested in halls 3 and 4. The following table shows preference wise income details. What would be the optimal assignment to maximize the total revenue ? (Figures in 1000)
 |
Halls |
|||
Parties |
1 |
2 |
3 |
4 |
A |
10 |
9 |
– |
– |
B |
8 |
10 |
8 |
5 |
C |
7 |
10 |
6 |
8 |
D |
10 |
8 |
– |
– |
         (Ans :  A ® 2, B ® 3, C ® 4, D ® 1; Revenue (1000) = 9 + 8 + 8 +  10 = 35)
One Comment