(Maximization)

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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)       Find worker machine combination that maximizes total output

(ii)      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)

 

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)

 

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)

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